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Q.
In a binomial distribution, the mean is $4$ and variance is $3$ . Then its mode is :
Probability - Part 2
Solution:
Given, mean $=4$ i.e., $np =4$
and variance $=3$, i.e., $npq=3$
so, $q=3 / 4$ and $p=1-q=1 / 4$
and $n =16$
Hence the Binomial distribution is given by
${ }^{16} C _{ r }\left(\frac{1}{4}\right)^{ r }\left(\frac{3}{4}\right)^{16- r } ; r =0,1, \ldots \ldots .16$
$\therefore $ Mode of the distribution is a number that repeats for the maximum time.
Thus, Mode $=4$.