Discrete distributions (cont'd)

Admistrivia:
- Passout answer to sample midterms
- Monday will be a review. Bring questions and problems.
- Reminder of extra office hours

Sums of Binomials

Sum of binomials is binomial:

Eg. X,Y are binomial, pi = 3/4, n = 5

Z = X + Y

Z is binomial pi = 3/4, n = 10

Easiest binomial is n = 1: mean = pi, var = pi(1 - pi)

Binomial: mean = n(pi), var = n(pi)(1-pi)

Sums of Poisson

Sum of poisson is poisson:

Eg. X = number males entering a bank, Y = number of females mu for males = 40, mu for females = 50

Z = X + Y

Z is Poisson mu 90

Discuss means and variances of each type

Binomial: mean = n(pi), var = n(pi)(1-pi)
Hypergeometric: mean = n(pi)(1-pi), var = n(pi)(1 - pi) (N-n)/(N-1)
Geometric: mean = 1/pi, var = (1 - pi)/pi²
Negative binomial: k/pi, var = k(1 - pi)/pi²
Poisson: mu, var = mu

Tuesday/Thursday evening ride:

Every Tuesday/Thursday evening a bunch of riders leave from the Art Museum at 6:30 for a 1 1/2 hour ride around the park (20 miles total). We always wait for people who get flats. We have 40 riders. Typically we two riders get 2 flats.

What is distribution of the number of riders who flat?
What is the probability of an evening without any flats?
Based on these numbers, how many flats would you expect to get when crossing the whole US? (say 4000 miles total)
- What is the expected number of flats?
- What is the distribution?
- What is the SD?
- How many tubes should you bring?

Last modified: Wed Nov 3 09:49:49 EST 1999