Question

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. does the table show a probability distribution? select all that apply. a. yes, the table shows a probability distribution. b. no, the random variable xs number values are not associated with probabilities. c. no, the sum of all the probabilities is not equal to 1. d. no, the random variable x is categorical instead of numerical. e. no, not every probability is between 0 and 1 inclusive. 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. \\( \mu= \\) child(ren) (round to one decimal place as needed.) b. the table does not show a probability distribution.

Explanation:

Step1: Check probability distribution conditions

• All \(P(x)\) values: \(0.034, 0.154, 0.312, 0.312, 0.154, 0.034\) are between \(0\) and \(1\).
• Sum of \(P(x)\): \(0.034 + 0.154+0.312 + 0.312+0.154 + 0.034=1\). So it is a probability distribution.

Step2: Calculate the mean \(\mu\)

The formula for the mean of a discrete probability distribution is \(\mu=\sum xP(x)\).

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Answer:

A. Yes, the table shows a probability distribution.
A. \(\mu = 2.5\) child(ren)