STA230/MTH230: Probability

Homework #4: Poisson & Hypergeometric

Text Problems are from Jim Pitman, Probability.

• Exercises
  

  § 2.4:		2	6	8
  § 2.5:		2	5	6	8	13
  § 2.R:		7	20*	33

  * Early printings of the text have a typographical error in Review Exercise 20 b) saying that the probability of correct transmission of a bit is p=0.01; others say (correctly) that q=0.01, and so p=0.99. Use the correct values.
• Another Problem
  Let X have a Poisson probability distribution with mean λ=6. Once you observe X, toss a fair coin X times and let Y be the number of heads that show. Find the probability that Y=4.
  
  For extra credit, let the Poisson random variable X above have an arbitrary mean λ>0 and find the probability that Y=y for every integer y≥0, where once again Y is the number of heads in X throws of a fair coin.
  
  

Good Luck!