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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:!

•A discrete random variable has a countable number of possible values •A continuous random variable takes all values in an interval of numbers. Probability Distributions of RVs Discrete Let X be a discrete rv. Then the probability mass function (pmf), f(x), of X is:! f(x)= Continuous!

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