Q. 84.4( 8 Votes )

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)

Answer :

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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