Transcription of Lecture 4: Random Variables and Distributions
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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:! F(x)=P(X"x)=f(y)dy#$x%pdfcdf! P(a"X"b)=F(b)#F(a)Using CDFs to Compute ProbabilitiesContinuous rv:! F(x)=P(X"x)=f(y)dy#$x%pdfcdf!
• Random Variables. Random Variables! "-1 0 1 A rv is any rule (i.e., function) that associates a number with each outcome in the sample space. Two Types of Random Variables •A discrete random variable has a countable number of possible values •A continuous random variable takes all values in an interval of numbers.
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