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If a random variable X has a binomial distribution B (8,1/2) then find X for which the outcome is the most likely.

Answer»

SOLUTION :GIVEN binomial distribution is B `(8.1/2)`
THUS n=8,p=`1/2,q=1/2`
We shall find X which is most likely i.e.for which p(x-r) is maximum where r=0,1,2,.......,8
As p=q, the probability is maximum when `^8C_r` is maximum
But `^8C_r`,r=0,1,2,....... 8 is maximum when r=4.
Thus the most likely OUTCOME is x=4.


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