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 
0 
1 
2 
3 
4 
5 


P(x) 
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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