 Apostol, section 14.16, problem 2.
 Apostol, section 14.16, problems 8 and 9
 Apostol, section 14.16, problem 14
 Apostol, section 14.18, problem 1, parts a,c,e and f
 Apostol, section 14.22, problem 3
 Apostol, section 14.24, problem 1
 Apostol, section 14.27, problem 3. Consider just the continuous case.
You may assume any wellknown general properties of integrals.
 Apostol, section 14.27, problems 4 and 5.
 Apostol, section 14.27, problem 10.
 You have acquired two atoms of a radioisotope that decays in accordance
with an exponential distribution whose decay constant is l.
 Let X and Y be random variables corresponding to the time after which atoms 1 and 2 respectively decay.
 a. Find a probability density for the random variable X  Y.
 b. What is the expectation of  X  Y?
 Apostol, section 14.27, problem 12.
 Let X and Y be independent random variables, each with a standard normal distribution.
Let Z = X^{2} + Y^{2}.
 a) Find a density function f_{Z}(t) for the random variable Z, and shetch a graph of this function.
 b) Find the expectation of Z.
 c) Find the value of t for which the density f_{Z}(t) has its maximum value.
 Suppose you write a function in C that does the following:
 1). Generate a random real number x with a uniform distribution in (0, c]
 2). Return the value y =  log(x) (natural logarithms, of course)
What is a probability density f_{Y}(y) for the output of this function?
 Assume that you have a function that generates random floatingpoint numbers in [0,1] with a uniform distribution.
 a) Invent a method to generate random floatingpoint numbers Y in [0,4] with a density function
proportional to the square root of Y.
 b) What is the probability that a random number generated by this method will be less than 1?
There are two ways to answer this question  using them both will provide a check of your answer.
