Lecture18 - AMS 312 April 26th , 2010 Inference on several...

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AMS 312 April 26 th , 2010 Inference on several proportions—the Chi-square test (large sample) Def. Multinomial Experiment. We have a total of n trials (sample size=n) 1 For each trial, it will result in 1 of k possible outcomes. 2 The probability of getting outcome i is  i p , and  1 k i i p = =1 3 These trials are independent. e.g. Previous experience indicates that the probability of obtaining 1 healthy calf from a mating is 0.83. Similarly, the probabilities of obtaining 0 and 2 healthy calves are 0.15 and 0.02 respectively. If the farmer breeds 3 dams from the herd, find the probability of getting exact 3 health calves. Def. Multinomial Distribution Let  i X  be the number of trials resulted in i-th category out of a total of n trials and  i p   be the probability of getting i-th category outcome, then 1 1 1 2 2 1 1 2 ! ( , ,..., ) ... ! !... ! k x x k k k k n P X x X x X x p p x x x = = = = Solution: n = 3, k = 3 Category 1: 0 healthy calf Category 2: 1 healthy calf Category 3: 2 healthy calves Note: K! = K*(K-1)*…3*2*1; 0! = 1; 1! = 1 1
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Lecture18 - AMS 312 April 26th , 2010 Inference on several...

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