Question

# Five males with a particular genetic disorder have one child each. The random variable x is...

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 1 2 3 4 5 0.01160.0116 0.08340.0834 0.23990.2399 0.34520.3452 0.24840.2484 0.07150.0715

Find the mean of the random variable x. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

muμequals=nothing

​(Round to one decimal place as​ needed.)

B.

The table is not a probability distribution.

Find the standard deviation of the random variable x. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

sigmaσequals=nothing

​(Round to one decimal place as​ needed.)

B.

The table is not a probability distribution.

The sum of all individual probabilities = 0.0116 + 0.0834 + 0.2399 + 0.3452 + 0.2484 + 0.0715 = 1

Since the sum of all probabilities is equal to 1, it is a probability distribution table.

Mean() = E(X) = 0 * 0.0116 + 1 * 0.0834 + 2 * 0.2399 + 3 * 0.3452 + 4 * 0.2484 + 5 * 0.0715 = 2.9

E(X^2) = 0^2 * 0.0116 + 1^2 * 0.0834 + 2^2 * 0.2399 + 3^2 * 0.3452 + 4^2 * 0.2484 + 5^2 * 0.0715 = 9.9117

Variance = E(X^2) - (E(X))^2

= 9.9117 - (2.9)^2

= 1.5017

Standard deviation () = = 1.2

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