Let X be a random variable following binomial distribution whose mean and variance are 200 and 160 respectively. What is the value of the number of trials (n)?

Explanation

For a binomial distribution, Mean = np = 200 and Variance = npq = 160. Dividing the two gives q = 160/200 = 4/5. Since p = 1 - q, we get p = 1/5. Substituting p back into the mean equation yields n(1/5) = 200 \implies n = 1000.

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