First slide

Random variable and probability distribution

Question

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

Difficult

A

34
B

32
C

33
D

67

Solution

$P (X = r) = 100_{C_{r}} {(\frac{2}{3})}^{100 - r} {(\frac{1}{3})}^{r}$
$\Rightarrow {(\frac{2}{3} + \frac{1}{3})}^{100} = {(\frac{2}{3})}^{100} {[1 + \frac{1}{2}]}^{100}$

$\Rightarrow \frac{(n + 1) | x |}{1 + | x |} = \frac{101}{3} = 33.3$

$∴$ r = 33

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