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Unformatted text preview: Lecture 8 Outline and Examples Examples of discrete random variablesHypergeometric distributionBernoulli trials and Binomial distribution Hypergeometric distribution Example: Random sampling without replacing. Random sampling is a statistical technique for gaining information about the composition of a large population. Take a sample of size n without replacement from a population of size N consisting of G good and B = N  G bad elements and let X = the number of good elements in a sample. Then, Hypergeometric distribution Example: Random sampling without replacing. Random sampling is a statistical technique for gaining information about the composition of a large population. Take a sample of size n without replacement from a population of size N consisting of G good and B = N  G bad elements and let X = the number of good elements in a sample. Then, P ( X = g ) = ( G g ) ( N G n g ) ( N n ) . Hypergeometric distribution Example: Random sampling without replacing. Random sampling is a statistical technique for gaining information about the composition of a large population. Take a sample of size n without replacement from a population of size N consisting of G good and B = N  G bad elements and let X = the number of good elements in a sample. Then, P ( X = g ) = ( G g ) ( N G n g ) ( N n ) . Recall that by convention: ( n k ) = 0 for k < 0 or k > n , so that P ( X = g ) 6 = 0 only for g = max (0 , n N + G ) , . . . , min ( n , G ). Binomial distribution Example: Random sampling with replacement. Take a sample of size n with replacement from a population of size N consisting of G good and B = N  G bad elements and let X = the number of good elements in a sample. Then, Binomial distribution Example: Random sampling with replacement. Take a sample of size n with replacement from a population of size N consisting of G good and B = N  G bad elements and let X = the number of good elements in a sample. Then, P ( X = g ) = Binomial distribution Example: Random sampling with replacement. Take a sample of size n with replacement from a population of size N consisting of G good and B = N  G bad elements and let X = the number of good elements in a sample....
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This note was uploaded on 06/05/2010 for the course STAT PStat 120a taught by Professor Rohinikumar during the Spring '10 term at UCSB.
 Spring '10
 RohiniKumar
 Bernoulli, Binomial

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