Answer to Question #213470 in Statistics and Probability for santi

Statistics and Probability

Question #213470

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

Expert's answer

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

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