SOLUTION: A six-sided die is rolled 4 times. Let the random variable x count the number of Three's. Construct a probability distribution for x. Find the mean and standard deviation

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Question 386746: A six-sided die is rolled 4 times.
Let the random variable x count the number of Three's. Construct a probability distribution for x.
Find the mean and standard deviation of the probability distribution.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let X = r.v. indicating the number of times 3 appears in 4 tries. Then the possible values of x are 0,1,2,3,4. This is a binomial experiment with n = 4, p = 1/6, and q = 5/6. The probability distribution is given by
p%28x%29+=+nCx%2A%285%2F6%29%5E%284-x%29%2A%281%2F6%29%5Ex.
The mean is given by mu+=+np+=+4%2A%281%2F6%29+=+2%2F3, and variance is
sigma%5E2+=+npq+=+4%2A%281%2F6%29%2A%285%2F6%29+=+5%2F9. Thus the standard deviation is sigma+=+sqrt%285%29%2F3.