Class 05 Discrete probability models

# Class 05 Discrete probability models - Models of discrete...

This preview shows pages 1–14. Sign up to view the full content.

T. R. Willemain MAU Spring 06 1 Models of discrete random variables

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
T. R. Willemain MAU Spring 06 2 Agenda PMF and CDF of discrete RVs Expectations of discrete random variables Frequently used models of discrete random variables In-class exercises Microquiz 05
T. R. Willemain MAU Spring 06 3 PMF and CDF

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
T. R. Willemain MAU Spring 06 4 PMF and CDF
T. R. Willemain MAU Spring 06 5 Mean and Variance

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
T. R. Willemain MAU Spring 06 6 Frequently used models Bernoulli : 0 or 1; models “coin flip” type situations Binomial : 0, 1… n; models “total # of heads in n flips” Poisson : 0, 1, 2, … ∞; models count of purely random events in fixed interval, e.g., # of emergencies in a day, # of cracks in 1 mile of sidewalk
T. R. Willemain MAU Spring 06 7 Bernoulli model Possible outcomes are binary: X = 0 or 1 live/die, work/fail, heads/tails Successive trials are “independent” i.e., what happens in one has no influence on next Constant probability of success P(X=1) = p so P(X=0) = 1-p Expectations E[X] = p V[X] = p(1-p)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
T. R. Willemain MAU Spring 06 8 Binomial model
T. R. Willemain MAU Spring 06 9 Risk Analysis of Tile Loss on the Space Shuttle

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
T. R. Willemain MAU Spring 06 10 Map of risk zones
T. R. Willemain MAU Spring 06 11 A binomial submodel for # of patches of tile loss

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
T. R. Willemain MAU Spring 06 12 Poisson model
T. R. Willemain MAU Spring 06

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 25

Class 05 Discrete probability models - Models of discrete...

This preview shows document pages 1 - 14. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online