Question

If x is a binomial random variable, compute p(x) for each of the following cases:

n=5, x=1, p = 0.2
n=4, x=2, q = 0.4
n=3, x=0, p = 0.7
n=5, x=3, p = 0.1
n=4, x= 2, q = 0.6
n=3, x=1, q = 0.9

Answer 1

P(x)=n!/ (x!(n−x)!) * p^x(1−p)^(n−x)
is the formula you have to evaluate for each number set.
Can you see where that takes you?
the n! Just means 1*2*....*n
So plug in the numbers and see what you get.

Answer 2

Let me walk you through the first example then
n=5, x=1, p = 0.2
We know P(x)=n!/ (x!(n−x)!) * p^x(1−p)^(n−x)
so 5!/(1! * (5-1)!) * 0.2^1 * (1-0.20)^(5-1)
= 120/24 * 0.2 * 0.8^4
= 0.4096