Stat 1430 4.3 Random Variables

notation

X,Y (capital letters)

mean of discrete random variables

a weighted average of the possible outcomes; weights are the probabilities

variance of discrete random variables

a weighted average of the squared deviations from the mean

random variable

any characteristic you can count, measure, or categorize whose values depend on chance

discrete random variables

finite list of possible values or countably infinite ex: X=number of heads on 2 coin flips(X=0,1,2) X=number of customers in a queue at the bank (X=0,1,2,3,4,5,6,....infinite)

continuous random variables

measures an amount of time uncountably infinite range of values as infinite as in interval on the real line Ex: time to help customers at help desk

linear transformation

that is multiply x by constant and add a constant Ex: 3+4x

requirments of discrete random variable

1.) 0<or equal p(x) < or equal 1 2.) sum of p(x)=1 ex: x=number of heads in 2 coin flips X=0,1,2 p(x) =x(0)=.25, x(1)=.50, x(2)=.25, all sum to 1