Week_6-7_Slides - Stat 2001 / Stat 6039 Week 6 Cumulative...

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Stat 2001 / Stat 6039 Week 6 Cumulative Distribution Functions Continuous Probability Distributions
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Last Week Discrete RV’s: Binomial, Bernoulli, Poisson, Geometric, Hypergeometric, Negative Binomial Poisson Approximation: Roll 2 dice 12 times. Find the probability of 0,1,2 double sixes. Mathematical Expectation: What is the expected value of an indicator variable? Moment Generating Functions: What two purposes do these generating functions serve?
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Moments Skewness is a measure of assymmetry. It requires calculation of the 3rd moment.
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Moments Kurtosis is a measure of “peaked-ness”. It requires calculation of the 4th moment.
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Dow Jones Industrial Average The leptokurtic tendency of the DJIA since 1973 can be seen by comparing the Dow Jones daily return (from 10/29/1993–4/19/2000) and the normal density with the same mean and st. dev.
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Cumulative Distribution Function (CDF) The (cumulative) distribution function (cdf) of a random variable Y is ( ) ( ) F y P Y y . Let Y be the number of heads that come up on 2 tosses of a coin. Find Y ’s cdf.
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If F ( y ) is a cdf then: 1. ( ) 0 F y as y   2. ( ) 1 F y as y   3. F ( y ) is nondecreasing. [[Also, 4. F ( y ) is right continuous. This means that for .]]
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Week_6-7_Slides - Stat 2001 / Stat 6039 Week 6 Cumulative...

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