1.9 lecture09

1.9 lecture09 - STAT 1301 Probability & Statistics...

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1 STAT 1301 Probability & Statistics Lecture 9 MGF Moment generating functions The moment generating function for a random variable X is M X ( t ) = E ( e tX ). Verify M (0) = Verify M X (0) = X . Likewise M X (0) = E( X 2 ). 22 (0) [ (0)] XX X MM  
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2 Binomial distribution The random variable X is said to have a Binomial distribution with parameters n and p. X ~ Binomial( n , p ) () ( ) (1 ) 0 ,..., xn x n f xP Xx pp   x   0 n nx n x x n ab x  Binomial MGF M X ( t ) = (1 – p + p e t ) n Poisson Experiment The experiment consists of counting the number ( X ) of times a certain event occurs during a given unit of time. The probability the event occurs in a given unit of time is the same for all units. The number of events that occur in one unit time is independent of the number that occur in other units. Example The number of customers per unit of time at a cashier’s counter in a bank.
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This note was uploaded on 05/04/2011 for the course STAT 1301 taught by Professor Smslee during the Spring '08 term at HKU.

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1.9 lecture09 - STAT 1301 Probability & Statistics...

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