PROBLEM 8E

In a smoking survey among boys between the ages of 12 and 17, 78% prefer to date nonsmokers, 1% prefer to date smokers, and 21% don’t care. Suppose seven such boys are selected randomly. Let X equal the number who prefer to date nonsmokers and Y equal the number who prefer to date smokers.

(a) Determine the joint pmf of X and Y. Be sure to include the support of the pmf.

(b) Find the marginal pmf of X. Again include the support.

Answer:

Step 1 of 2 :

Given,

In a smoking survey among boys between the ages of 12 and 17.

Here 78% prefer to date non smokers.

78% = 0.78

1% prefer to date smokers.

1% = 0.01 and

21% don’t care.

21% = 0.21

We know that seven boys are selected randomly.

Let X equal the number who prefer to date non smokers and

Let Y equal the number who prefer to date smokers .

PMF(x,y) = Prob {X prefer non smokers, Y prefer smokers}

Our goal is to find

a). Determine the joint pmf of X and Y.Be sure to include the support of the pmf.

b).Find the marginal pmf of X.Again include the support.

a).

Now we have to determine the joint pmf of X and Y.

We know that prefer to date non smokers is 0.78, prefer to date smokers is 0.01,don’t care is 0.21 and n=7.

Then the joint pmf X and Y is

Where

Hence the the joint pmf of X and Y is above.