The random variable of X is the number of girls of fourchildren born to a couple

Question

The random variable of X is the number of girls of fourchildren born to a couple that is equall likely to have either aboy child or a girl child. Its probability distribution is asfollows
x 0 1 2 3 4 P(X=x) 0.0625 0.2500 0.3750 0.2500 0.0625
a. Find and interpret the mean of the randomvariable. b. obtain the standard deviation of the random variableby using one of the formulas given c. draw a probability histogram for the random variable;locate the mean; and show one, two, and three standard-deviationintervals.

The random variable of X is the number of girls of fourchildren born to a couple that is equall likely to have either aboy child or a girl child. Its probability distribution is asfollows
P(X=x) 0.0625 0.2500 0.3750 0.2500 0.0625
a. Find and interpret the mean of the randomvariable. b. obtain the standard deviation of the random variableby using one of the formulas given c. draw a probability histogram for the random variable;locate the mean; and show one, two, and three standard-deviationintervals.

Explanation / Answer

(b) E(X)=0*0.0625+1* 0.2500+ 2* 0.3750+3* 0.2500+4* 0.0625 =2 E(X^2)=0*0.0625+1^2* 0.2500+ 2^2* 0.3750+3^2* 0.2500+4^2* 0.0625=5 Var(X) = E(X^2) - [E(X)]^2            = 5 - 2^2            =1 So the standard deviation is Var(X) = 1

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