Answer to Question #213470 in Statistics and Probability for santi

Question

Suppose x has the pmf f(x)={kx for x=1,2,3,4

{0,elsewhere

Find the value of the constant k hence obtain the mean and the variance of x

Answer 1

$$k(1)+k(2)+k(3)+k(4)=10k=1$$

$$k=0.1$$

$$mean=E[X]=1(0.1)+2(0.2)+3(0.3)+4(0.4)=3$$

$$E[X^2]=1^2(0.1)+2^2(0.2)+3^2(0.3)+4^2(0.4)=10$$

$$V(X)=E[X^2]-(E[X])^2=10-(3)^2=1$$