I.  In a shipment of 10 missiles, there are 3 defectives whose
engines will not fire.  Out of the shipment, 4 missiles are
selected at random. 
\item{A)}  What is the probability that all 4 will fire?
\item{B)}  What is the probability that at most 2 will not fire?
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II.  In a biomedical research experiment, the survival time $Y$
in weeks of an animal exposed to a certain fatal disease is a random variable
with a gamma distribution with $\alpha = 2$ and $\beta = 6$.
\item{A)} What is the mean survival time of a randomly selected exposed animal?
\item{B)} The cost of treating an exposed animal is $C = 10 + .1 Y^2$.
Find the mean and variance of $C$.
\item{C)} If 6 exposed animals are chosen at random, what is the probability
that at least two survive for 15 or more weeks?
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III.  The lifetime of a certain type of small motor is normally distributed
with mean 10 years and standard deviation 2 years.  The manufacturer
replaces free all motors that fail while under warrantee.  But to 
avoid going out of business because of the cost of doing the 
free replacements, the manufacturer must set the warrantee so that
no more than 3\% of the motors that fail will be covered.  What
should the length of the warrantee be?
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IV.  
\item{A)}  Let $Y$ be a binomial random variable based on $n$ trials
with success probability $p$.  Find the moment-generating function 
of $X = aY + b$, where $a, b$ are constant.
\item{B)}  Let $Z$ be a standard normal random variable. What is the 
moment-generating function for $Y = Z^2$?
What type of random variable is $Y$?
(Hint:  You will want to assume that $1 - 2t > 0$ and use
the substitution $u = \sqrt{1 - 2t}\cdot y$ to evaluate the integral
for $E(e^{tY})$.)
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