) Let X be a discrete random variable with the values x=0,1,2 and Let the probabilities be P(X=0)=0.25 P(X=1)=0.50 P(X=2)=0. Calculate E(X) b.Find...

1.) Let X be a discrete random variable with the values x=0,1,2 and Let the probabilities be

P(X=0)=0.25

P(X=1)=0.50

P(X=2)=0.25

a. Calculate E(X)

b.Find E(X^2)

c. Find Var(X)

d. Given a new function

g(X)=3X+2

2.)Find the expectation and variance of this function.

XP(X)EX=X*P(X)E(X^2)X^*P(X) 2) 00.25000 E(X)=SUM(X*P(X))VAR(X)=SUMX^2*P(X)-E(X)^2 10.5 g(X)=3X+2E(X)=3*1+2=VAR(X)=3^2*(.5)+0 54.5 10.50.510.5 20.250.541 11.5