Question

For one statistics course, among the students who purchase textbook, 70% choose physical textbook, 30% choose electronic textbook. Assume three students who made the purchases are randomly selected. Let random variable X be the number of students chosen physical textbook minus the number of students chosen electronic textbook.

1. find the probability distribution of X.

2. calculate P(X=0) and P(X=3).

3. Find the mean of X

Answer 1

Let A be the number of students who purchase physics textbooks.

B be the number of students who purchase electronics textbooks.

So X = A - B

When A = 0 B = 3 So X = -3

When A = 1 B = 2 So X = -1

When A = 2 B = 1 So X = 1

When A = 3 B = 0 So X = 3

So X has 4 possible values -3,-1,1,3.

1) The probability distribution of X

Here A follows Binomial distribution with parameters n = 3 and p=0.7

So we will find probability distribution of X from probability distribution of A

P(X = -3)

= P(A = 0)

P(X = -1)

= P(A = 1)

P(X = 1)

= P(A = 2)

P(X = 3)

= P(A = 3)

So probability distribution of X is

X	P(X)
-3	0.027
-1	0.189
1	0.441
3	0.343

2)

P(X = 0 ) = 0

P(X = 3) = 0.343

3)

E(X) = x*P(x)

​Please give thumbs up if you like the answer.