Answer to Question #299297 in Statistics and Probability for Xai

Question

Let X be a ramdom variable with the following probability distribution

x: 1, 2, 3, 4

P(X=x): 0.4, 0.3, 0.2, 0.1

a. Find E(X) and Var(X)

b. is E(X) a possible value of X

Answer 1

a. $E(X)=1*0.4+2*0.3+3*0.2+4*0.1=2.$

$Var(X)=1^2*0.4+2^2*0.3+3^2*0.3+4^2*0.1-2^2=1.9.$

b. E(X) is a possible value of X.