From a lot of 12 items containing 3 defectives, a sample of 5 items is drawn at random. Let the random variable X denote the number of defective items in the sample. Let items in the sample be drawn o

Question

From a lot of 12 items containing 3 defectives, a sample of 5 items is drawn at random. Let the random variable X denote the number of defective items in the sample. Let items in the sample be drawn one by one without replacement. If variance of X is n m ​ , where gcd ( m , n ) = 1 , then n − m is equal to _________

TestHub · Accepted Answer

​ a = 1 − 12 C 5 ​ 3 C 5 ​ ​ b = 3 ⋅ 12 C 5 ​ 9 C 4 ​ ​ c = 3 ⋅ 12 C 5 ​ 9 C 3 ​ ​ d = 1 ⋅ 12 C 5 ​ 9 C 2 ​ ​ u = 0. a + 1. b + 2 ⋅ c + 3 ⋅ d = 1.25 σ 2 = 0. a + 1. b + 4. c + 9 d − u 2 σ 2 = 176 105 ​ ​ Ans. 176 − 105 = 71

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