02_14 - STAT 400 Examples for 02/14/2011 Spring 2011 4....

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STAT 400 Examples for 02/14/2011 Spring 2011 4. Suppose that on Halloween 6 children come to a house to get treats. A bag contains 8 plain chocolate bars and 7 nut bars. Each child reaches into the bag and randomly selects 1 candy bar. Let X denote the number of nut bars selected. a) Is the Binomial model appropriate for this problem? b) Find the probability that exactly 2 nut bars were selected. Hypergeometric Distribution : N = population size, S = number of “successes” in the population, N S = number of “failures” in the population, n = sample size. X = number of "successes" in the sample when sampling is done without replacement. Then n x n x N S N S X C C C N S N S n x n x x - - = - - = = ) ( P OR ( ) ( ) + - + - - - - - - - - - + - + - - - = = 1 1 1 1 1 1 1 1 P n x n x x x x x n x N S N ... N S N N S N N S ... N S N S X max(0, n + S N ) x min( n , S ). EXCEL: = HYPGEOMDIST( x , n , S , N ) gives P(X = x )
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5. A jar has N marbles, S of them are orange and N S are blue. Suppose 3 marbles are selected. Find the probability that there are 2 orange marbles in the sample, if the selection is done … with replacement without replacement a) N = 10, S = 4; b) N = 100, S = 40; c) N = 1,000, S = 400; Binomial Hypergeometric with replacement without replacement Probability ( ) x n x ) X p p x n x - - = = 1 P( -
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This note was uploaded on 02/24/2011 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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02_14 - STAT 400 Examples for 02/14/2011 Spring 2011 4....

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