A couple plans to have children until they get a girl, but they agree they will not have more than three children, even if all are boys. Assume that the probability of having a girl is
0.50.5.
Let X be a random variable indicating how many children the couple will have. Find the standard deviation of the random variable X.
x 
11 
22 
33 


P(X=x) 
0.5000.500 
0.2500.250 
0.250 
Solution :
Mean = = X * P(X)
= 1 * 0.50 + 2 * 0.25 + 3 * 0.25
= 0.50 + 0.50 + 0.75
= 1.75
Standard deviation =
=X ^{2} * P(X)  ^{2}
= 1 * 0.50 + 2^{2} * 0.25 + 3^{2} * 0.25  1.75^{2}
= 0.6875
= 0.8292
Standard deviation = 0.8292
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