Question

2. Find the mean and standard deviation of the hypergeometric distribution with the parameters n=3, a=4, and N=8 (a) By first calculating the necessary probabilities to get the hypergeometric distribution (20 points) (b) Use the general formulas and calculate the mean and standard deviation using the original equations; (10points) (c) By using the special formulas for the mean and the variance of a hypergeometric distribution (10points)

Answer 1

hypergunbie The Probability density of distribution is given by PC X = n). (A) (N-2) hire a 4, N=8, n = 3 .. PC x = k) = ( 4 ). ( 3 ) = 0,123 (A) P(x=0). (2) (1) 7/6 - TA P(x-1). (A) (2 - 46 - 24 P(x2). 0) . p(x-3) (4). 18

=> [(*)-ng944 SD Cx) = na wa) 48 = V N (1) 3x 4 x 4 8x7 = 0.9258 94.99091284 56 (c) N-1 Mean= p = np Variance np (P) N-a where poa Solving Mean= 3/2 and Variance = 48/56= 0.8571