MA340 Quiz: July 25-26, 2013. Name: Student number:
Instructions: Due in my o▯ce by 4:00 PM on Friday, July 26. Slip it under the door if I am not in. Please don’t
hand in the ▯rst draft of your answer - i.e. solve the problems and then write up clear, easy-to-follow solutions in
the space provided.
1. Let X have probability mass function
f(x) = (:3)(:7) ; x = 1;2;3;::: :
Derive the moment generating function of X. Be sure to state (atd justify) its domain.
Hint: At some point you’re going to want to factor out (:3)e from each term in a series. 2. Suppose that X has moment generating function
M (t) = ; t < ln(10) :
X 1 ▯ (:1)e
(a) Use M X (or a suitable transformation oX M ) to ▯nd the mean and variance of X.
(b) Use M X (or a suitable transformation oX M ) to ▯nd the mean and variance of Y = e .
(c) Use MX (or a suitable transformation oX M ) to ▯nd the moment generating function of Z = 4X ▯ 1. 3. Suppose I play three rounds of a certain game, and that I have a 75% chance of winning any round (the outcome
of any given round has