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Lecture 4: Random Variables and Distributions

Lecture 4: RandomVariables and DistributionsGoals Working with Distributions in R Overview of discrete and continuousdistributions important in genetics/genomics Random VariablesRandom Variables ! "01-1A rv is any rule ( , function) that associatesa number with each outcome in the samplespaceTwo Types of Random Variables A discrete Random variable has acountable number of possible values A continuous Random variable takes allvalues in an interval of numbersProbability Distributions of RVsDiscreteLet X be a discrete rv. Then the probability mass function (pmf), f(x),of X is:! f(x)=P(X = x), x 0,x Continuous! P(a"X"b)=f(x)dxab#Let X be a continuous rv. Then the probability density function (pdf) ofX is a function f(x) such that for any two numbers a and b with a b:abAaUsing CDFs to Compute ProbabilitiesContinuous rv:!

•Before data is collected, we regard observations as random variables (X 1,X 2,…,X n) •This implies that until data is collected, any function (statistic) of the observations (mean, sd, etc.) is also a random variable •Thus, any statistic, because it is a random variable, has a probability distribution - referred to as a sampling ...

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