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…

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 ^2, then 96 ^2 is equal to______

Accepted Answer

Correct answer: 56. (56) X= denotes number of defective x 0 1 2 3 P (x ) 715 512 512 112 x_1 ^2 0 1 4 9 P_ix_1 ^2 0 512 2012 912 p_ix_i 0 512 1012 312 = _P_ix_i= 1812 _P_ix_1^2= 3412 ^2= _P_ix_1^2- ( )^2 = 3412- ( 1812 )^2= 176- 94 34-2712= 71296 ^2=96 712=56

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

Solution

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