Consider a random variable X with the following moment generating function:
(a) Find the expected value of $3 - X$.
(b) Find variance of $3 - X$.
What I have reached till now is that is (most probably?) geometric distribution which means that the probability is 0.2, and that if we want to get the expected value of $3 - X$ then it would be equal to $E(3-X) = E(3) - E(X)$
What I think: E(X) = 1/0.2 But I have no idea where to go from there.
Edit: OKAY, I GOT THIS TILL NOW! :D
a) $E(3-X) = E(3) - E(2Y) = E(3) - 2 * E(Y) = 3 - 2 * 1/0.2 = -7$ (I also used differentiation rule to double check, but differentiation is way longer)
I tried to use a similar logic to solve (b), since the variance = $p/(1-p)^2$ I thought I could equate $Var(X) = Var(2Y) = 2 * (0.8/0.2^2) = 40$
Not sure if this method is right or not, though..
LAST EDIT! XD
Answer of B: Okay, so, $Var(X) = Var(2Y) = 2^2 Var(Y) = 4 * (0.8/0.2^2) = 80$
Thank you all! :)