Answer to Question #119574 in Statistics and Probability for Kay Cliff

Question

A discrete random variable has probability mass function, P(X = n) = 12
n.
Let Y =  1, for x even
 1, for x odd
Find the expected value of Y ; (E[y]).

Answer 1

P_y(1)=P(x is even) 1/2n even when n multiples of 4, so P(x is even)=1/4=0.25 - every fourth number

P_y(-1)=1-0.25=0.75

E(Y)=0.25*1+0.75*(-1)=-0.50