Question #137b9
1 Answer
Mean shown here; variance is similar.
Explanation:
We begin with the mean (expected value) of a discrete distribution.
That is, the mean is the sum of value x probability for each outcome.
For a binomial distribution, there are only two outcomes: success and failure. Let p be the probability of success. Let n be the number of trials.
Let
From the probability density function for the Binomial Distribution, we have
For the Binomial Distribution,
Note that the sum is from r = 1 to n, since the value is zero if r = 0.
Regarding the sum, we are summing the binomial over all possible outcomes. Since the binomial distribution is a probability distribution, the sum over all outcomes is 1.
Therefore,