Probability*Distributions

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3Probability Distributions(Ch , , , , )2Probability distribution FunctionsProbability distribution function(pdf): Function for mapping random variables to real numbers. Discrete random variable: Values constitute a finite or countablyinfinite random variable:Set of possible values is the set of real numbers R, one interval, or a disjoint union of intervals on the real line. 3Random VariablesNotation! variables - usually denoted by uppercase letters near the end of our alphabet ( X, Y). value - now use lowercase letters, such as x, which correspond to the !"=$=1&''()( + ,$-$=1&''()( + Properties of PDFsFor f(x) to be a legitimate pdf, it must satisfy the following two (x) 0 for all discrete continuous random Variables6The pdf of a discrete X describeshow the total probability is distributed among all the possible range values of the X:f(x) = p(X=x), for each value x in the range of XPDFs for Discrete RVs7Example A lab has 6 computers.))

2 Probability,Distribution,Functions Probability*distribution*function (pdf): Function,for,mapping,random,variablesto,real,numbers., Discrete*randomvariable:

  Distribution, Probability, Random