Question

If X is a binomial random variable with expected value 6 and variance 2.4. Find the
probability of X=5.

Answer 1

The expected value np=6

Variance npq=2.4

q=$\frac{npq} {np} =\frac {2.4}{6}$ =0.4

p=1-0.4=0.6

np=6=n*0.6

n=$\frac {6}{0.6}$ =10

P(X=5)

$P(X=x) =\binom {n} {x} p^x (1-p)^{n-x}$

$P(X=5) =\binom {10}{5}*0.6^5 *0.4^5$

=0.2007