Let X ∼ Bin(7, 0.3). Find

a. P(X = 1)

b. P(X = 2)

c. P(X < 1)

d. P(X > 4)

e. μx

f.

Answer :

Step 1 of 7:

Let X follows binomial distribution with probability mass function is

P(x: n,p) = (1 - p , x = 0, 1, 2, ….., n.

We have binomial distribution with n = 7 and p = 0.3

Step 2 of 7:

The claim is to find the P(x = 1)The probability mass function is

P(x: n,p) = (1 - p , x = 0, 1, 2, ….., n.

Where, n = 7, p = 0.3 and x = 1

Therefore, P(x = 1) = (1 - 0.3

= (7) (0.3) (0.11765)

= 0.2471

Hence, P(x = 1) = 0.2471

Step 3 of 7:

The claim is to find the P(x = 2)The probability mass function is

P(x: n,p) = (1 - p , x = 0, 1, 2, ….., n.

Where, n = 7, p = 0.3 and x = 2

Therefore, P(x = 2) = (1 - 0.3

= (21) (0.09) (0.16807)

= 0.3176

Hence, P(x = 2) = 0.3176.

Step 4 of 7:

The claim is to find the P(x < 1) = P( x = 0)The probability mass function is

P(x: n,p) = (1 - p , x = 0, 1, 2, ….., n.

Where, n = 7, p = 0.3 and x = 0

Therefore, P(x = 0) = (1 - 0.3

= (1) (1) (0.08235)

= 0.08235

Hence, P(x < 1) = 0.08235.