If X is a binomial distribution with parameters n = 100 and p=13 then pX=r is maximum when ___

q+pnTr+1=ncrqn−rprpx=r is maximum thenr=np Where is G. I. F.r=100×13=33.33r=33

If X is a binomial distribution with parameters n = 100 and p=13 then pX=r is maximum when ___

q+pnTr+1=ncrqn−rprpx=r is maximum thenr=np Where is G. I. F.r=100×13=33.33r=33

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If X is a binomial distribution with parameters n = 100 and $p = \frac{1}{3}$ then $p (X = r)$ is maximum when ___

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answer is C.

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Detailed Solution

${(q + p)}^{n}$
$T_{r + 1} = n c_{r} q^{n - r} p^{r}$
$p (x = r)$ is maximum then

$r = [n p]$ Where is G. I. F.
$r = [100 \times \frac{1}{3}] = [33.33]$
$r = 33$

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If X is a binomial distribution with parameters n = 100 and $p = \frac{1}{3}$ then $p (X = r)$ is maximum when ___