# 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(xi), xi = 0,1,2,3,4,5,6)

As per the question,

X is any random variable whose binomial distribution is   Thus, P(X = x) = nCxqn-xpx , where x = 0, 1, 2, …n  It can be clearly observed that P(X = x) will be maximum if 6cx will bw maximum.

6cx = 6c6 = 1

6c1 = 6c5 = 6

6c2 = 6c4 = 15

6c3 = 20

Hence we can clearly see that 6c3 is maximum.

for x = 3, P(X = x) is maximum.

Hence, proved that the most likely outcome is x = 3.

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