Question

# Five males with an​ X-linked genetic disorder have one child each. The random variable x is...

 x ​P(x) Five males with an​ X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the​ X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is​ given, find its mean and standard deviation. If a probability distribution is not​ given, identify the requirements that are not satisfied. 0 0.035 1 0.157 2 0.308 3 0.308 4 0.157 5 0.035

Does the table show a probability​ distribution? Select all that apply.

A.

​Yes, the table shows a probability distribution.

B.

​No, not every probability is between 0 and 1 inclusive.

C.

​No, the random variable​ x's number values are not associated with probabilities.

D.

​No, the sum of all the probabilities is not equal to 1.

E.

​No, the random variable x is categorical instead of numerical.

Solution :

The sum of the probability is equal to 1 .

P(X) = 1

A.

​Yes, the table shows a probability distribution.

 x P(x) x * P(x) x2 * P(x) 0 0.035 0 0 1 0.157 0.157 0.157 2 0.308 0.616 1.232 3 0.308 0.924 2.772 4 0.157 0.628 2.512 5 0.035 0.175 0.875 Sum 1 2.5 7.548

Mean = = X * P(X) = 2.5

Standard deviation =

=X 2 * P(X) - 2

=  7.548 - 2.52

= 1.1393

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