Five males with a particular genetic disorder have one child

Five males with a particular genetic disorder have one child each. The random variable x is the number of children among the five who inherit the genetic disorder. Determine whether the table describes a probability distribution. If it does, find the mean and standard deviation.

x P(x)
0 0.0380
1 0.1755
2 0.3240
3 0.2990
4 0.1380
5 0.0255

A. Find the mean of the random variable x.

B.Find the standard deviation of the random variable x

Solution

As the sum of P(X) is 1, then it is a discrete probability distribution.

Thus,

a)

Thus, E(X) = 2.4 [ANSWER]

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b)

Also,

Var(x) = E(x^2) - E(x)^2 =    1.248  

s(x) = sqrt [Var(x)] =    1.117139204 [ANSWER]