If x is a binomial random variable, compute p(x) for each

Solution 43E

Step1 of 7:

Let us consider a random variable ‘X’ it follows binomial distribution with parameters ‘n and p.’

Here our goal is:

a). We need to find P(x), when n = 5, x = 1, p = 0.2

b). We need to find P(x), when n = 4, x = 2, q = 0.4

c). We need to find P(x), when n = 3, x = 0, p = 0.7

d). We need to find P(x), when n = 5, x = 3, p = 0.1

e). We need to find P(x), when n = 4, x = 2, q = 0.6

f). We need to find P(x), when n = 3, x = 1, p = 0.9

Step2 of 7:

a).

Here random variable ‘X’ it follows binomial distribution.

That is,

X B(n, p)

X B(5, 0.2)  

We know that the probability mass function of binomial distribution is:

                      x = 0,1,2,...,n.

Consider,

Hence,

Step3 of 7:

b).

Here random variable ‘X’ it follows binomial distribution.

That is,

X B(n, p)

X B(4, 0.4)  

We know that the probability mass function of binomial distribution is: