Question

Suppose X has a binomial distribution. Show that X = 3 is the most likely outcome.

(Hint: P(X = 3) is the maximum among all P (x_i), x_i = 0, 1, 2, 3, 4, 5, 6)

Answer 1

X is the random variable whose binomial distribution is.

Therefore, n = 6 and

It can be seen that P(X = x) will be maximum, if will be maximum.

The value ofis maximum. Therefore, for x = 3, P(X = x) is maximum.

Thus, X = 3 is the most likely outcome.