Question

Suppose x is a binomial distribution with parameters n = 100 and p = 1/2 then P(X=r) is maximum when r =

• A. 50
• B. 32
• C. 33
• D. 67

Answer 1

The correct option is A 50

${1/2}^n$

In binomial distribution system

n=100,p=1/2

P(X=r)=${}^{100}{C}_r$*${1/2}^r\ast {1/2}^{n-r}$

=${}^{100}{C}_r$*${\left(1/2\right)}^n$

${}^n{C}_r$ is maximum at r=n/2

Therefore,${}^{100}{C}_r$ is maximum at r=100/2=50

P(X=r) is maximum when r = 50