`! s _J_90f ` @ hn 8 x}RJ@w6MZ0BPbQ-l)||B-\g&`MsL. < Y`O.A*$jwy9RLIZ'`. Axioms of Probability The sum of all the probabilities of outcomes within a single sample space equals one: The probability of a complex event equals the sum of the probabilities of the outcomes making up the event: The probability of 2 independent events equals the product of their individual probabilities: Probability distributions We use probability distributions because they fit many types of data in the living world Ex. In our example, it describes the probability to get a 1, the probability to get a 2 and so on. If you want to Save Ppt Discrete Random Variables And Probability . 1O_3vg Suppose a couple plan to have 3 children and are interested in the number of girls they might have. Denition 5 Let X be a random variable and x R. 1. Fundamentals of Probability. Free access to premium services like Tuneln, Mubi and more. We've updated our privacy policy. << Determine if the following are discrete or continuous random variables: a. Named after the Swiss mathematician Jacob Bernoulli, the Bernoulli distribution is a discrete probability distribution of a single binary random variable, which either takes the value 1 or 0. Webinar: Estratgias para comprar componentes eletrnicos em tempos de escassez, SE2023 0207 Software Architectural Design.pptx, SE2023 0401 Software Coding and Testing.pptx, KCD Italy 2022 - Application driven infrastructure with Crossplane, SE2023 0201 Software Analysis and Design.pptx, Re:cap do AWS re:Invet 2022 for Data Engineer and Analytics, No public clipboards found for this slide, Enjoy access to millions of presentations, documents, ebooks, audiobooks, magazines, and more. Learn faster and smarter from top experts, Download to take your learnings offline and on the go. iT+QHxS~^n;4 stream Discrete Random Variables and Probability Distributions - . /Width 1 12 0 obj Normal Distribution. 1.1 Indicator Random Variables For x = 5 we have 658 and this is -0.5. It has millions of presentations already uploaded and available with 1,000s more being uploaded by its users every day. /Filter[/CCITTFaxDecode] Activate your 30 day free trialto continue reading. 1] 0,
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r.=D~m7Sx?k_6R'}&iT8WOyUV#fHY (Z-\D' J_e|~UWOu - Chapter 5: DISCRETE RANDOM VARIABLES AND THEIR PROBABILITY DISTRIBUTIONS RANDOM VARIABLES Discrete Random Variable Continuous Random Variable RANDOM VARIABLES cont - This PPT is based on continuous random variable and joint distribution of random variable. Ppt Discrete Random Variables And Probability Distributions images that posted in this website was uploaded by Opta.libero.pe.Ppt Discrete Random Variables And Probability Distributions equipped with a HD resolution x .You can save Ppt Discrete Random Variables And Probability Distributions for free to your devices.. Looks like youve clipped this slide to already. Illustrate random variable 2. Random Variable.pptx - Free download as Powerpoint Presentation (.ppt / .pptx), PDF File (.pdf), Text File (.txt) or view presentation slides online. The probability density function looks like a bell-shaped curve. kanchala sudtachat. is also a random variable Thus, any statistic, because it is a random variable, has a probability distribution - referred to as a sampling . Fundamentals of Probability The probability P that an outcome occurs is: The sample space is the set of all possible outcomes of an event Example: Visit = { (Capture), (Escape)} Axioms of Probability The sum of all the . 1.4 Discrete Random Variables and Probability Distributions

. They'll give your presentations a professional, memorable appearance - the kind of sophisticated look that today's audiences expect. 4. probability density functions. /BitsPerComponent 1 8 0 obj Continuous Random Variables and Probability Distributions - 4. continuous random variables and probability distributions. - Random Variables Random Variables What you ll learn What is a Random Variable? endobj Facts and Features. A function can serve as the probability distribution for a discrete random variable X if and only if it s values, f(x), satisfythe conditions: a: f(x) 0 for each value within its domain b: P x f(x)=1, where the summationextends over all the values within its domain 1.5. Practice: Distributions with Mathematica, - Title: Initial probability distribution for Sam s sister child birth: singletons-2/3, twins 1/3. random variables - random responses corresponding to subjects randomly, Random Variables and Probability Distributions - . 2 Types: Discrete random variables Continuous random variables, The Binomial DistributionBernoulli Random Variables Imagine a simple trial with only two possible outcomes: Success (S) Failure (F) Examples Toss of a coin (heads or tails) Sex of a newborn (male or female) Survival of an organism in a region (live or die) Jacob Bernoulli (1654-1705), The Binomial DistributionOverview Suppose that the probability of success is p What is the probability of failure? 16 . Exercise Next, we will perform an exercise in R that will allow you to work with some of these probability distributions! The probability that Z is less than -2.20 is _____. If X is a continuous random variable then b a P a X b . CrystalGraphics 3D Character Slides for PowerPoint, - CrystalGraphics 3D Character Slides for PowerPoint, - Beautifully designed chart and diagram s for PowerPoint with visually stunning graphics and animation effects. The functions C and M are examples of random variables. 149. ( ) 0, . Subinterval [5,6] Subinterval [3,4] Uniform Random Variables The probability density function (PDF). Instant access to millions of ebooks, audiobooks, magazines, podcasts and more. If we catch one of these fish in Monterey Bay, What is the probability that it will be at least. 2023 SlideServe | Powered By DigitalOfficePro, Random Variables and Probability Distributions, - - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -. Because normal distributions apply only to continuous variables, we need other types of distributions to model discrete variables. Download Now, Chapter 3: Random Variables and Probability Distributions, Chapter 6: Binomial Probability Distributions, Section 4 Random Variables and Probability Distributions, Topic 4: Discrete Random Variables and Probability Distributions, Chapter 11 Discrete Random Variables and their Probability Distributions, Chapter 5 Discrete Probability Distributions, Chapter 8 Probability and Random variables, Random Variables & Probability Distributions, Discrete Random Variables and Probability Distributions, Distributions of Random Variables ( 4.6 - 4.10), Random Variables and Probability Distributions, Probability: The Study of Randomness Random Variables. Example 64 deaths in 20 years out of thousands, If we substitute ?/n for p, and let n approach, The Poisson distribution is applied when random, Deviation from a Poisson distribution may, Rutherford, Geiger, and Bateman (1910) counted. 4.2 Variance and Covariance of Random Variables The variance of a random variable X, or the variance of the probability distribution of X, is de ned as the expected squared deviation from the expected value. chapter 3: discrete random variables and probability distributions 3 6.Roll two dice and record the sum of the number of pips showing. 2/ Given that X is a normally distributed variable with a mean of 50 and a standard deviation of 2, find the probability that X is between 47 and 54. ;C*h40#9&$@#ae9?\!(m/W5HKCCQ6i'fhh4^{_U4@zB^L!X-Lc tI'P8>N+1^qfAGVw9 << /S /GoTo /D (section.2) >> Probability Distributions - A listing of the possible outcomes and their probabilities (discrete r.v.s) or their densities (continuous r.v.s) Normal Distribution - Bell-shaped continuous distribution widely used in statistical inference Sampling Distributions - Distributions corresponding to sample statistics (such as mean and proportion . By whitelisting SlideShare on your ad-blocker, you are supporting our community of content creators. Q3 Random Variables and. Distinguishes between a discrete and a continuous random variable 3. Do their data follow a Poisson distribution? 'D%[6WU}WXirSyiaj\Q& 3/ A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Chapter 4: Random Variables and Probability Distributions Author: Joe Nowakowski Last modified by: Muskingum College Created Date: 7/26/2007 11:27:32 AM . discrete and continuous, Random Variables and Discrete probability Distributions - . ( ) 0, . 6. 1 , . Instant access to millions of ebooks, audiobooks, magazines, podcasts and more. Random Variables and Probability Distributions Modified from a presentation by Carlos J. Rosas-Anderson. in n trials, and n! Learn faster and smarter from top experts, Download to take your learnings offline and on the go. Weve updated our privacy policy so that we are compliant with changing global privacy regulations and to provide you with insight into the limited ways in which we use your data. Discrete Random Variables and Probability Distributions - 3. discrete random variables and probability distributions. We've encountered a problem, please try again. We've updated our privacy policy. Height (cm) of Hypericum cumulicola at Archbold Biological Station. random variables - random outcomes corresponding to subjects randomly. Create stunning presentation online in just 3 steps. Variance & Standard Deviation Let X be a random variable with probability distribution f(x) and mean m. The variance of X is s2 =Var(X) =E . definition:a rule that assigns one (and only one), Random Variables and Probability Distributions - . A probability distribution is used to determine what values a random variable can take and how often does it take on these values. Distributions. It provides the probabilities of different possible occurrences. That it will be no more than 32 in. Loosely speaking, we can think of the Bernoulli distribution as a model giving the set of possible outcomes for a single experiment, that can be answered . And theyre ready for you to use in your PowerPoint presentations the moment you need them. The Normal DistributionLength of Fish That its length will be between 26 and 29 inches? endobj Introduction to random variables and probability distributions. content. Consider a sequence of n Bernoulli trials, with probability p of success. The Normal DistributionLength of Fish What is the probability that it will be at least 31 in. Moments of Variables and Vectors. _Aak5yVXray>}``c3$z@DP\mKU!k>E{_#SmO#+}YlLFUu>Y@WU+`! &\FU&;h x]QMKQ=M2PuRh+W$ChJHF:$2fv3F%Q Lecture4_Distributions.ppt Author: Josh Akey Created Date: 4/10/2008 8:18:03 PM . A random variable is a numerical description of the outcome of a statistical experiment. Uploaded by Vernadette Gail Dela Cruz. STATISTICS Random Variables and Probability Distributions - . The distribution covers the probability of real-valued events from many different problem domains, making it a common and well-known distribution, hence the name "normal."A continuous random variable that has a normal distribution is said . Let Sn be the random variable whose value is the number of successes in the sequence of n component trials. In this video You will find, the "Hand Written Notes of Random Variables and Probability Distribution". 147. If so, share your PPT presentation slides online with PowerShow.com. - not so perfect Arm Strength Versus Grip Strength Negative Correlation Child Labor versus GDP Extreme Correlation 1 Linear than two variables Random Variables and Probability Distributions. - Chapter 7 Random Variables and Discrete probability Distributions 7.2 Random Variables and Probability Distributions A random variable is a function or rule that - Probability Distribution Probability Distributions: Overview To understand probability distributions, it is important to understand variables and random variables. The only caveats are that the sample size must be large enough and that the observations themselves must be independent and all drawn from a distribution with common expectation and variance. - Discrete Probability Distributions * Larson/Farber 4th ed Larson/Farber 4th ed Larson/Farber 4th ed Larson/Farber 4th ed Larson/Farber 4th ed Larson/Farber 4th ed Engineering Mathematics Probability Distribution - Department of Applied Sciences & Engineering. This is given by the probability density and mass functions for continuous and discrete random variables, respectively. If X is a continuous random variable, then X has, Consequently, the probability of any particular, To calculate the probabilities associated with a, To calculate E(X), we let ?x get infinitely small. random variables - random outcomes corresponding to subjects, Discrete Probability Distributions (Random Variables and Discrete Probability Distributions) - . For instance, a random variable representing the . An example of the binomial distribution is the. Looks like youve clipped this slide to already. (n 1) ? Download Free PPT. Random Variables and Discrete probability Distributions - 7-2. random variables. The probability P that an outcome occurs is, The sample space is the set of all possible, The sum of all the probabilities of outcomes, The probability of a complex event equals the sum, The probability of 2 independent events equals, We use probability distributions because they fit, many variables relevant to biological and, Because normal distributions apply only to, The mathematical rule (or function) that assigns, Imagine a simple trial with only two possible, Survival of an organism in a region (live or die), Suppose that the probability of success is p, Roll of a die (S 1) p 0.1667 ? ( ) 1 , . Consider two random variables X and Y Let X~N(,) and let Y=aX+b where a and b are constants Change of scale is the operation of multiplying X by a constant a because one unit of X becomes a units of Y. p(x) 0 for all values of x p(x) = 1 6 - Probability Distributions, Information about the for Time The majority of Poisson applications are related to the number of Distribution Functions (p.d.f DISCRETE RANDOM VARIABLES AND THEIR PROBABILITY DISTRIBUTIONS. Arial Narrow Century Wingdings Garamond Times New Roman Book Antiqua Arial Symbol Larson & Farber MathType 5.0 Equation Discrete Probability Distributions 4.1 Random Variables Random Variables Discrete Probability Distributions Constructing a Discrete Probability Distribution Constructing a Discrete Probability Distribution Constructing a . Random Variables and Probability Distributions - . >> XP(X) e. Construct a histogram for the probability distribution in the space below. a. P(X)X 3 4/9 6 2/9 9 1/9 12 1/9 15 1/ b. P(X)X 1 3/10 2 1/10 3 1/10 4 2/10 5 3/ c. XP(X) 20 1 30 0 40 0 50 0. endobj /Height 1 9 0 obj endobj P(Sn = k) = C(n, k)pk(1 p)n k 0 k n. Quiz 3: 5 questions Practice what you've learned, and level . /Decode[1 0] Now customize the name of a clipboard to store your clips. The Poisson DistributionEmission of -particles Calculation of : = No. statistical experiment. Enjoy access to millions of ebooks, audiobooks, magazines, and more from Scribd. long? Defined for a closed interval (for example. professor ke-sheng cheng department of bioenvironmental, Random Variables and Discrete probability Distributions - 2. Weve updated our privacy policy so that we are compliant with changing global privacy regulations and to provide you with insight into the limited ways in which we use your data. << /S /GoTo /D (section.3) >> Probability distributions Most people are familiar with the Normal Distribution, BUT many variables relevant to biological and ecological studies are not normally distributed! 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In your PowerPoint presentations the moment you need them this video we help you learn What is probability. With 1,000s more being uploaded by its users every day we catch one these...: discrete random Variables for x = 5 we have 658 and this is given by the probability to a! - 7-2. random Variables and probability Distributions < br / > than -2.20 is _____ Distributions apply only to Variables... Record the sum of the outcome of a clipboard to store your clips functions for continuous and discrete probability -... Notes of random Variables? \ an exercise in R that will allow you to work with some these... To millions of ebooks, audiobooks, magazines, and the difference discrete! Probability density and mass functions for continuous and discrete probability Distributions - 4. random. < Determine if the following are discrete or continuous random Variables What you ll learn a. N Bernoulli trials, with probability P of success if we catch one of these probability Distributions - less!

. They'll give your presentations a professional, memorable appearance - the kind of sophisticated look that today's audiences expect. 4. probability density functions. /BitsPerComponent 1 8 0 obj Continuous Random Variables and Probability Distributions - 4. continuous random variables and probability distributions. - Random Variables Random Variables What you ll learn What is a Random Variable? endobj Facts and Features. A function can serve as the probability distribution for a discrete random variable X if and only if it s values, f(x), satisfythe conditions: a: f(x) 0 for each value within its domain b: P x f(x)=1, where the summationextends over all the values within its domain 1.5. Practice: Distributions with Mathematica, - Title: Initial probability distribution for Sam s sister child birth: singletons-2/3, twins 1/3. random variables - random responses corresponding to subjects randomly, Random Variables and Probability Distributions - . 2 Types: Discrete random variables Continuous random variables, The Binomial DistributionBernoulli Random Variables Imagine a simple trial with only two possible outcomes: Success (S) Failure (F) Examples Toss of a coin (heads or tails) Sex of a newborn (male or female) Survival of an organism in a region (live or die) Jacob Bernoulli (1654-1705), The Binomial DistributionOverview Suppose that the probability of success is p What is the probability of failure? 16 . Exercise Next, we will perform an exercise in R that will allow you to work with some of these probability distributions! The probability that Z is less than -2.20 is _____. If X is a continuous random variable then b a P a X b . CrystalGraphics 3D Character Slides for PowerPoint, - CrystalGraphics 3D Character Slides for PowerPoint, - Beautifully designed chart and diagram s for PowerPoint with visually stunning graphics and animation effects. The functions C and M are examples of random variables. 149. ( ) 0, . Subinterval [5,6] Subinterval [3,4] Uniform Random Variables The probability density function (PDF). Instant access to millions of ebooks, audiobooks, magazines, podcasts and more. If we catch one of these fish in Monterey Bay, What is the probability that it will be at least. 2023 SlideServe | Powered By DigitalOfficePro, Random Variables and Probability Distributions, - - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -. Because normal distributions apply only to continuous variables, we need other types of distributions to model discrete variables. Download Now, Chapter 3: Random Variables and Probability Distributions, Chapter 6: Binomial Probability Distributions, Section 4 Random Variables and Probability Distributions, Topic 4: Discrete Random Variables and Probability Distributions, Chapter 11 Discrete Random Variables and their Probability Distributions, Chapter 5 Discrete Probability Distributions, Chapter 8 Probability and Random variables, Random Variables & Probability Distributions, Discrete Random Variables and Probability Distributions, Distributions of Random Variables ( 4.6 - 4.10), Random Variables and Probability Distributions, Probability: The Study of Randomness Random Variables. Example 64 deaths in 20 years out of thousands, If we substitute ?/n for p, and let n approach, The Poisson distribution is applied when random, Deviation from a Poisson distribution may, Rutherford, Geiger, and Bateman (1910) counted. 4.2 Variance and Covariance of Random Variables The variance of a random variable X, or the variance of the probability distribution of X, is de ned as the expected squared deviation from the expected value. chapter 3: discrete random variables and probability distributions 3 6.Roll two dice and record the sum of the number of pips showing. 2/ Given that X is a normally distributed variable with a mean of 50 and a standard deviation of 2, find the probability that X is between 47 and 54. ;C*h40#9&$@#ae9?\!(m/W5HKCCQ6i'fhh4^{_U4@zB^L!X-Lc tI'P8>N+1^qfAGVw9 << /S /GoTo /D (section.2) >> Probability Distributions - A listing of the possible outcomes and their probabilities (discrete r.v.s) or their densities (continuous r.v.s) Normal Distribution - Bell-shaped continuous distribution widely used in statistical inference Sampling Distributions - Distributions corresponding to sample statistics (such as mean and proportion . By whitelisting SlideShare on your ad-blocker, you are supporting our community of content creators. Q3 Random Variables and. Distinguishes between a discrete and a continuous random variable 3. Do their data follow a Poisson distribution? 'D%[6WU}WXirSyiaj\Q& 3/ A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Chapter 4: Random Variables and Probability Distributions Author: Joe Nowakowski Last modified by: Muskingum College Created Date: 7/26/2007 11:27:32 AM . discrete and continuous, Random Variables and Discrete probability Distributions - . ( ) 0, . 6. 1 , . Instant access to millions of ebooks, audiobooks, magazines, podcasts and more. Random Variables and Probability Distributions Modified from a presentation by Carlos J. Rosas-Anderson. in n trials, and n! Learn faster and smarter from top experts, Download to take your learnings offline and on the go. Weve updated our privacy policy so that we are compliant with changing global privacy regulations and to provide you with insight into the limited ways in which we use your data. Discrete Random Variables and Probability Distributions - 3. discrete random variables and probability distributions. We've encountered a problem, please try again. We've updated our privacy policy. Height (cm) of Hypericum cumulicola at Archbold Biological Station. random variables - random outcomes corresponding to subjects randomly. Create stunning presentation online in just 3 steps. Variance & Standard Deviation Let X be a random variable with probability distribution f(x) and mean m. The variance of X is s2 =Var(X) =E . definition:a rule that assigns one (and only one), Random Variables and Probability Distributions - . A probability distribution is used to determine what values a random variable can take and how often does it take on these values. Distributions. It provides the probabilities of different possible occurrences. That it will be no more than 32 in. Loosely speaking, we can think of the Bernoulli distribution as a model giving the set of possible outcomes for a single experiment, that can be answered . And theyre ready for you to use in your PowerPoint presentations the moment you need them. The Normal DistributionLength of Fish That its length will be between 26 and 29 inches? endobj Introduction to random variables and probability distributions. content. Consider a sequence of n Bernoulli trials, with probability p of success. The Normal DistributionLength of Fish What is the probability that it will be at least 31 in. Moments of Variables and Vectors. _Aak5yVXray>}``c3$z@DP\mKU!k>E{_#SmO#+}YlLFUu>Y@WU+`! &\FU&;h x]QMKQ=M2PuRh+W$ChJHF:$2fv3F%Q Lecture4_Distributions.ppt Author: Josh Akey Created Date: 4/10/2008 8:18:03 PM . A random variable is a numerical description of the outcome of a statistical experiment. Uploaded by Vernadette Gail Dela Cruz. STATISTICS Random Variables and Probability Distributions - . The distribution covers the probability of real-valued events from many different problem domains, making it a common and well-known distribution, hence the name "normal."A continuous random variable that has a normal distribution is said . Let Sn be the random variable whose value is the number of successes in the sequence of n component trials. In this video You will find, the "Hand Written Notes of Random Variables and Probability Distribution". 147. If so, share your PPT presentation slides online with PowerShow.com. - not so perfect Arm Strength Versus Grip Strength Negative Correlation Child Labor versus GDP Extreme Correlation 1 Linear than two variables Random Variables and Probability Distributions. - Chapter 7 Random Variables and Discrete probability Distributions 7.2 Random Variables and Probability Distributions A random variable is a function or rule that - Probability Distribution Probability Distributions: Overview To understand probability distributions, it is important to understand variables and random variables. The only caveats are that the sample size must be large enough and that the observations themselves must be independent and all drawn from a distribution with common expectation and variance. - Discrete Probability Distributions * Larson/Farber 4th ed Larson/Farber 4th ed Larson/Farber 4th ed Larson/Farber 4th ed Larson/Farber 4th ed Larson/Farber 4th ed Engineering Mathematics Probability Distribution - Department of Applied Sciences & Engineering. This is given by the probability density and mass functions for continuous and discrete random variables, respectively. If X is a continuous random variable, then X has, Consequently, the probability of any particular, To calculate the probabilities associated with a, To calculate E(X), we let ?x get infinitely small. random variables - random outcomes corresponding to subjects, Discrete Probability Distributions (Random Variables and Discrete Probability Distributions) - . For instance, a random variable representing the . An example of the binomial distribution is the. Looks like youve clipped this slide to already. (n 1) ? Download Free PPT. Random Variables and Discrete probability Distributions - 7-2. random variables. The probability P that an outcome occurs is, The sample space is the set of all possible, The sum of all the probabilities of outcomes, The probability of a complex event equals the sum, The probability of 2 independent events equals, We use probability distributions because they fit, many variables relevant to biological and, Because normal distributions apply only to, The mathematical rule (or function) that assigns, Imagine a simple trial with only two possible, Survival of an organism in a region (live or die), Suppose that the probability of success is p, Roll of a die (S 1) p 0.1667 ? ( ) 1 , . Consider two random variables X and Y Let X~N(,) and let Y=aX+b where a and b are constants Change of scale is the operation of multiplying X by a constant a because one unit of X becomes a units of Y. p(x) 0 for all values of x p(x) = 1 6 - Probability Distributions, Information about the for Time The majority of Poisson applications are related to the number of Distribution Functions (p.d.f DISCRETE RANDOM VARIABLES AND THEIR PROBABILITY DISTRIBUTIONS. Arial Narrow Century Wingdings Garamond Times New Roman Book Antiqua Arial Symbol Larson & Farber MathType 5.0 Equation Discrete Probability Distributions 4.1 Random Variables Random Variables Discrete Probability Distributions Constructing a Discrete Probability Distribution Constructing a Discrete Probability Distribution Constructing a . Random Variables and Probability Distributions - . >> XP(X) e. Construct a histogram for the probability distribution in the space below. a. P(X)X 3 4/9 6 2/9 9 1/9 12 1/9 15 1/ b. P(X)X 1 3/10 2 1/10 3 1/10 4 2/10 5 3/ c. XP(X) 20 1 30 0 40 0 50 0. endobj /Height 1 9 0 obj endobj P(Sn = k) = C(n, k)pk(1 p)n k 0 k n. Quiz 3: 5 questions Practice what you've learned, and level . /Decode[1 0] Now customize the name of a clipboard to store your clips. The Poisson DistributionEmission of -particles Calculation of : = No. statistical experiment. Enjoy access to millions of ebooks, audiobooks, magazines, and more from Scribd. long? Defined for a closed interval (for example. professor ke-sheng cheng department of bioenvironmental, Random Variables and Discrete probability Distributions - 2. Weve updated our privacy policy so that we are compliant with changing global privacy regulations and to provide you with insight into the limited ways in which we use your data. << /S /GoTo /D (section.3) >> Probability distributions Most people are familiar with the Normal Distribution, BUT many variables relevant to biological and ecological studies are not normally distributed! 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