Lecture3_Chap3Pt2

# Lecture3_Chap3Pt2 - Lecture4 DiscreteDistributions

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Lecture 4 Discrete Distributions

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Special Discrete Distributions Bernoulli Distribution Binomial Distribution Negative Binomial Distribution Geometric Distribution Hypergeometric Distribution Poisson Distribution
Reminders… Bernoulli Distribution  X = 0, 1; P(X = 1) = p. Binomial Distribution X = the number of ‘successes’ in n  independent bernoulli trials each with  probability of success, p.

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Differing Variability Q: For which value(s) of  p  is the variance  of a Bernoulli random variable  maximized? Minimized?
Binomial continued What is the sample space of X ~ B(n,p)? What is the probability distribution of X?

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Probability Distribution
Expectation of B(n,p)

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Variance of B(n,p)
Example A beloved family of 10 rats is  mysteriously ill.  We find a webpage that  advertises a 90% effective rat medicine.   We buy 10 doses and administer  immediately! How many rats do we expect to be  cured?  What is the variance?

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Example continued Find P(X=4) Find P(X=E(X))
Continued Find P(X<9) Find P(X>=2)

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Continued The medicine is administered to all 10  rats.  Tomorrow 9 of them are dead.  Do  you think the scientists are correct  about the 90% effectiveness?
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## Lecture3_Chap3Pt2 - Lecture4 DiscreteDistributions

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