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

a. In order to find the mean (expectation) of the given distribution, we will use the following formula:

=xp(x)

So, first we need to multiply each value of X by each probability P(X), then add these results together. In this example we have:

=02073/10000+11917/5000+2709/2500+31049/10000+497/5000+57/5000=13499/10000

b. In order to find the standard deviation of the given distribution, we will use the following formula:

=x^2p(x)^2

Now we will find the sum:

x^2p(x)=0^22073/10000+1^21917/5000+2^2709/2500+3^21049/10000+4^297/5000+527/5000=28073/10000

Putting all together we have:

=x^2p(x)^2=28073/10000(13499/10000)^2=98506999/1000000000.9925

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