Question

. Roll a 6 sided die which is unbalanced so that the probability is 2/9 for each odd number, and the probability is 1/9 for each even number . define a RV X=the number which shows.

a. Find the expectd value of X. (leave as a fraction in lowest terms.)

b. find the variance of X. give the anwer as decimal rounded to the nearest ten-thousandth.

Answer 1

as P(odd number)=P(X=1)=P(X=3)=P(X=5)=2/9

P(even number)=P(X=2)=P(X=4)=P(X=6)=1/9

xP(x) 2/9 2/9 2/3 4/9 11/9 2/3 3 1/3 x2P(x) 0.22 0.44 2.00 1.78 5.56 4.00 14.00 P(x) 1/9 1/9 1/9 total 2xP(x) = Ex2P(x) E(x) = E(x2) Var(x)-o2 (x2)-(E(x))2- std deviation oVơ2- 3.33 14.00 2.89 1.700

a) expectd value of X=10/3

b)

variance of X =2.8889