Discrete distributions

• Admistrivia:
  • Extra problems to do for "fun"
  • You should 5.1 - 5.3 carefully
  • Collect homework 4
  • Passout homework 4 solutions

Bernoulli trials and binomial distributions

• Opinion poll: God exists vs God doesn't exist

• Call a 10 people and ask: are you G or D?

• Series might look like: D,D,D,G,D,G,G,D,G,D

• Let pi = P(God) and 1 - pi = P(D)

• Prob of series is: pi*pi*pi*(1-pi)*pi*...*pi

• How many series have exactly 6 "Gods" out of 10 trials? 10 choose 6.

Hypergeometric

• Better opinion poll: Don't ask the same person twice!

• Ask 10 out of 120 Ph.D. students in math department at U. MD.

• Suppose 55 actually believe in God, 65 don't

• Prob of getting 6 out of 10 believing in God?

• counting posibilites:
  • From the 55 choose 6 (ways of getting God fearing)
  • From the 65 choose 4 (ways of getting heathens)
  • From the 100 choose 10 (ways of getting anybody)

Geometric

• Days until I get run over by a bus. Notice it is the first time it happens that is important to me, not the second time.

• Success = run over

• P(Success) = pi

• What I hope for: (1-pi)*(1-pi)*(1-pi)*(1-pi)*(1-pi)....(1-pi)*pi

Negative binomial

• Days until I get "car door'ed" twice. At which point I learn not to ride in the door lane.

• (1-pi)*(1-pi)*...*pi*.....*(1-pi)*pi

• Look up formula if you need it

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

Last modified: Mon Nov 1 08:33:14 EST 1999