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 ______

Step-by-step solution

X= denotes number of defective array |c|c|c|c|c| x & 0 & 1 & 2 & 3 P ( x ) & 7 15 & 5 12 & 5 12 & 1 12 x ₁ ^2 & 0 & 1 & 4 & 9 P _ i x ₁ ^2 & 0 & 5 12 & 20 12 & 9 12 p _ i x _ i & 0 & 5 12 & 10 12 & 3 12 array = p _ i x _ i = 18 12 aligned & p _ i x ₁^2= 34 12 & ^2= p _ i x ₁^2-( )^2 aligned aligned & = 34 12 - ( 18 12 )^2= 17 6 - 9 4 & 34-27 12 = 7 12 & 96 ^2=96 7 12 =56 aligned