From a lot of 10 items, which include 3 defective items, a sample of 5 items is drawn at random. Let the random variable X denote the number of defective items in the sample. If the variance of X is σ

Question

From a lot of 10 items, which include 3 defective items, a sample of 5 items is drawn at random. Let the random variable X denote the number of defective items in the sample. If the variance of X is σ 2 , then 96 σ 2 is equal to ______

TestHub · Accepted Answer

X = denotes number of defective x P ( x ) x 1 ​ 2 P i ​ x 1 ​ 2 p i ​ x i ​ ​ 0 15 7 ​ 0 0 0 ​ 1 12 5 ​ 1 12 5 ​ 12 5 ​ ​ 2 12 5 ​ 4 12 20 ​ 12 10 ​ ​ 3 12 1 ​ 9 12 9 ​ 12 3 ​ ​ ​ μ = Σ p i ​ x i ​ = 12 18 ​ ​ Σ p i ​ x 1 2 ​ = 12 34 ​ σ 2 = Σ p i ​ x 1 2 ​ − ( μ ) 2 ​ ​ = 12 34 ​ − ( 12 18 ​ ) 2 = 6 17 ​ − 4 9 ​ 12 34 − 27 ​ = 12 7 ​ 96 σ 2 = 96 × 12 7 ​ = 56 ​

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