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 sum of all the probabilities is not equal to 1.
c. no, not every probability is between 0 and 1 inclusive.
d. no, the random variable x is categorical instead of numerical.
e. no, the random variable xs number values are not associated with probabilities.

Explanation:

Step1: Check probability range

All values of \(P(x)\) are between \(0\) and \(1\) inclusive (\(0.033\geq0\), \(0.163\geq0\), \(0.304\geq0\)).

Step2: Check sum of probabilities

\(\sum_{x = 0}^{5}P(x)=0.033 + 0.163+0.304 + 0.304+0.163+0.033 = 1\)

Step3: Check variable type

The random - variable \(x\) (number of children with disorder) is numerical.

Since all requirements for a probability distribution are met.

Answer:

A. Yes, the table shows a probability distribution