SAMPLE PROBLEMS FROM VARIOUS EXAMS                 MATH 340
_____________________________________________________________________________

1. All the screws in a machine come from the same factory but it is twice as 
   likely to be from Factory A as from Factory B. The percentage of defective
   screws is 5% from A and 2% from B.  Two screws are inspected. If the first
   is found to be good, what is the probability that the second is also good?

2. Consider a seq of iid r.v.'s X_i, i \geq 1, with a Poisson dist with para-
   meter \alpha=2.  Let S_n = X_1 + ... + X_n.

   a. Specify the range and the formula for the dist of X_i.
   b. Derive a formula for the generating function of X_i.
   c. Using the formula in (b) calculate the mean and the S.D. of X_i.
   d. What is the generating function for S_n?
   e. Using the function in (d) calculate the prob the S_n=3, the mean, and
   the SD of S_n.
   f. What does the CLT tell us about the dist of S_n? Explain?
   g. Find an estimate for P(167 \leq S_100 \leq 205)?

3. A pair of distinguishable dice are rolled once. Let X denote the product of 
   the numbers facing up.

   a. Specify the range and the dist of X. (This is called Einstein stat.)
   b. Calculate the expected value of X.
   c.Calculate P(9 < X \leq 15).