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Chapter 12: Q. 12.60 (page 502)

In this exercise, you are to consider two variables, xand ydefined on a hypothetical population. Following are the conditional distributions of the variable ycorresponding to each value of the variablex.
a. Are the variables xandy associated? Explain your answer.
b. Determine the marginal distribution ofy.
c. Can you determine the marginal distribution of x? Explain your answer.

Short Answer

Expert verified

(a) No, they are not associated the conditional distribution for y given x are same for all values of x.

(b) The marginal distribution of yis :

1-0.422,2-0.211,3-0.047,4-0.004Total=1NA=1000

(c) No, we cannot determine the mrginal distribution of x from the given data.

Step by step solution

01

Part (a) Step 1. Given Information.

the variables x, ydefined on hypothetical population.

02

Part (a) Step 2. Find if the variables are associated.

No, they are not associated the conditional distribution fory givenx are same for all values ofx.

03

Part (b) Step 1. Marginal distribution of y.

Marginal distribution of y is same as the conditional, distribution of y for any given value of x.

The marginal distribution of y is:

1-0.422,2-0.211,3-0.047,4-0.004Total=1NA=1000

04

Part (c) Step 1. Marginal distribution of x.

No, we cannot determine the mrginal distribution of x from the given data.

There are two distribution of xthat are compatible with the given data.

1. NB=1000,NC=1000,NZ where x = zis the number of samples with Z鈭�{A,B,C}whereNA=1000.

2. NB=1000,NC=1000,NC=1000

These two cases are compatible with the given data but the marginals of x are different.

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