4 For The Geometric Distribution With Probability Mass Function Pmf F X 0 0 1 0 X X 0 1 2 0 0 1 1 (124.1 KiB) Viewed 30 times
4. For the geometric distribution with probability mass function (pmf) f(x;0) = 0(1 – 0), X x = 0, 1, 2, ..., 0) < 0 <1, i= en Ji= מת For this distribution, the maximum likelihood estimator is ên = n/(n + 2?–1 X;). The test statistic used in the generalized likelihood ratio test is given by (a) 2 log LR = 2 [25-1 1; log (6) + (n – ?–1 log (1-00 (b) 2 log LR 2 21=1 <; log + n log (1)] (c) 2 log LR = 2 log | d92 (6" (1 – 3)2 - x)] (d) 2 log LR = 2log [(n log(0) + 2?_1 ; log(1 – 6))] (e) 2 log LR = 2 [n log (%) + 2?_1 Ti log (15%)] ; ( i= 00 d2 X = 1 d d02 п - A i=
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log (1-00 (b) 2 log LR 2 21=1 <; log + n log (1)] (c) 2 log LR = 2 log | d92 (6" (1 – 3)2 - x)] (d) 2 log LR = 2log [(n log(0) + 2?_1 ; log(1 – 6))] (e) 2 log LR = 2 [n log (%) + 2?_1 Ti log (15%)] ; ( i= 00 d2 X = 1 d d02 п - A i=