Find the standard deviation of the random variable 22 The pr

Find the standard deviation of the random variable. 22) The probabilities that a batch of 4 computers will contain 0,1,2,3, and 4 defective computers are 0.6474,0.3102,0.0575,0.0047, and 0.0001, respectively. Round the answer to two decimal places.

Solution

mean = E(X) = sum of (X * P(X) = 0.4397

variance = E(X^2) - mean^2 = 0.5841 - 0.4397^2 = 0.39076391

standard deviation = sqrt(variance) = 0.63

hence A is the correct choice

X	P(X)	X^2	X*P(X)	X^2*P(X)
0	0.6274	0	0	0
1	0.3102	1	0.3102	0.3102
2	0.0575	4	0.115	0.23
3	0.0047	9	0.0141	0.0423
4	0.0001	16	0.0004	0.0016
sum			0.4397	0.5841