Question

If X be B.V. with $E\left(X\right)=5$ and $E\left(X^2\right)-{E\left(X\right)}^2=4$ then the parameters of distribution are

• A. $\frac{1}{4},20$
• B. $\frac{1}{5},20$
• C. $\frac{1}{5},25$
• D. $\frac{4}{5},25$

Answer 1

Answer: (C)

$\frac{1}{5},25$

Here $E\left(X\right)=$ Mean
$=np$ and
$E\left(x^2\right)-E(x{)}^2=$ Variance
$=np(1-p)$
Here $n=$ no.of trials while p is the probability of success.
Hence $np=5$
$np(1-p)=4$
$5(1-p)=4$
$1-p=\frac{4}{5}$
$p=\frac{1}{5}$
Therefore $n=5\left(5\right)$
$=25$
Hence the parameters are
$\frac{1}{5},25$