Question

In: Statistics and Probability

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

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.

x   P(x)
0   0.029
1   0.164
2   0.307
3   0.307
4   0.164
5   0.029

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

A

Yes table shows a probability distribution.

B.

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

C.

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

D.

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

E.

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

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.

nothing

A. ​u =. child(ren) ​(Round to one decimal place as​ needed

B. The table does not show 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. O=   child(ren) ​(Round to one decimal place as​ needed.)
B. The table does not show a probability distribution.

Solutions

Expert Solution

Solution :

x P(x) x * P(x) x2 * P(x)
0 0.029 0 0
1 0.164 0.164 0.164
2 0.307 0.614 1.228
3 0.307 0.921 2.763
4 0.164 0.656 2.624
5 0.029 0.145 0.725
Sum 1 2.5 7.504

A) Yes table shows a probability distribution.

Mean = = X * P(X) = 2.5

Standard deviation =

=X 2 * P(X) - 2

=  7.504 - 2.52

= 1.1


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