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

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) (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
.
The mean is given by , and variance is
. Thus the standard deviation is .
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