Five males with a particular genetic disorder have one child each. The random va

Question

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. 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. mu = (Round to one decimal place as needed.) 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. sigma = (Round to one decimal place as needed.) The table is not a probability distribution.

Explanation / Answer

The probabilities add up to 1, so it is a probability distribution.

Consider:

Thus,  
  
E(x) = Expected value = mean = Sum(xP(x)) =    4.0501 = 4.1 [ANSWER, MEAN]

*************************

As

Var(x) = E(x^2) - E(x)^2 =    0.76898999

Then

s(x) = sqrt [Var(x)] =    0.876920743 = 0.9 [ANSWER]

x P(x) x P(x) x^2 P(x) 0 0.0002 0 0 1 0.0053 0.0053 0.0053 2 0.045 0.09 0.18 3 0.1919 0.5757 1.7271 4 0.4089 1.6356 6.5424 5 0.3487 1.7435 8.7175

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