Question

If a random variable $x$ has a binomial distribution $B(8,\frac{1}{2})$, then find $x$ for which the outcome is more likely.

Answer 1

So, $n=8,p=1/2$

Now probability distribution for the value of $x=k$

$P(x=k){=}^8{C}_k\left(\frac{1}{2}{)}^k\right(1-\frac{1}{2}{)}^{-k+8}=\frac{{}^8{C}_k}{2^8}$

$P(x=k)$ will be maximum for $k=4$

Hence $x=4$.