Whenever a certain experiment is performed either outcome ti or outcome h occurs and these 2 outcomes arc equally likely. X and Y are 2 discrete random variables defined on S = {t ₁ , t ₂ } such that t ₁ when occurs, X has the value 0 and Y has the value 3 whereas when t ₂ occurs, X and Y both have the value 1. This gives the mean and variance of X as

while the mean and variance of Y arc E(Y)= 2 and V(Y)= 1 This information is summarized below. Are X and Y independent random variables?

A Yes

a. No

c. Cannot be determined

Discrete random variable X has E(X) = 5 and V(X) = 3. Discrete random variable Y has E(Y) = 2 and V(Y) =1. If X and Y arc independent random variables, and W = 2X - 4Y, find V (W).

A. -4

B. -2

c. 2

D. 10

E(X)== and V(X) = 2 outcome 1 12 probability .5 .5 value of X value of Y 0 3 1 1 E(X)=.5 V(X)=.25 E(Y) = 2 V(Y) = 1