ch05

Distribution Families
• Named family of distributions characterized by a single pdf with one or more parameters.
– Normal distribution  parameters: , 

• The different distribution families often have theoretical reasons for being used in different practical cases:
– Normal: measurement & dimension data
– Lognormal: manual service & repair times
– Poisson: # of events occurring in a time period, distance, or area – Exponential, Weibull: Time to failure of equipment

Ch. 5: Discrete Distributions
1. Uniform
2. Binomial
3. Hypergeometric
4. Negative Binomial
5. Geometric
6. Poisson
SKIPPING: Multinomial (p/149-150)

Discrete Uniform Distribution

Bernoulli Process

Binomial Distribution

f(x;n,p)=

=average number of successes in n trials

Binomial Tables (in text)

Problem
• The probability that a patient recovers from a delicate heart operation is 0.9. What is the probability that exactly 5 of the next 7 patients having this operation survive?

Negative Binomial Distribution

k

p k (1  p)
  p2 2

Note: Not in textbook Problem
The probability that a patient recovers from a delicate heart operation is 0.9.
• What is the probability that the 7th patient is the 5th patient to survive the operation?
• On average, how many patients will undergo the surgery before a patient does not survive?

Binomial vs. Negative Binomial
Binomial

Negative Binomial

• Based on Bernoulli process
• Probability of x successes in n trials

• Based on Bernoulli process
• Probability of trial x being the kth success

• Focus: # successes

• Focus: # trials

 n b( x : n, p)    p x q n  x
 x

 x  1 k xk b *( x : k , p)   p  q
 k  1

Geometric Distribution
• Special case of negative binomial
• Focus: finding the trial of the 1st success
• Example: “What is the chance that it will take
5 trials before a success occurs?”

Geometric Distribution

Example
Suppose the probability is 0.8 that any given person will believe a tale about the transgressions of a