Question

let x be a binomial random variable. use the formula to compute the following probabilities;

(a) p(x=2), if n=8 and p=0.1

(b) p(x=5), if n=9 and p=0.5

(c) p(x=9), if n=10 and p=0.95

Answer 1

$P_x=C^x_np^xq^{n-x}$

a.q=1-p=0.9

$C^2_80.1^20.9^6=\frac{8!}{2!6!}0.01x0.531441=0.1488$

b. $C^5_90.5^50.5^4=\frac{9!}{5!4!}0.03125x0.0625=0.246$

c.

$C^9_{10}0.95^90.05^1=\frac{10!}{9!1!}0.63x0.05=0.315$