Question: For three categorical variables X, Y, and Z: a. Prove that mutual independence of X, Y, and Z implies that X and Y are both

For three categorical variables X, Y, and Z:

a. Prove that mutual independence of X, Y, and Z implies that X and Y are both marginally and conditionally independent.

b. When X is independent of Y and Y is independent of Z, does it follow that X is independent of Z? Explain.

c. When any pair of variables is conditionally independent, explain why there is no three-factor interaction.

Step by Step Solution

★★★★★

3.39 Rating (171 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a For mutual independence ijk i j k Summing both si... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Categorical Data Analysis Questions!

Q:

Suppose that X, Y, and Z are three random variables such that Var(X) = 1, Var(Y) = 4, Var(Z) = 8, Cov(X, Y) = 1, Cov(X, Z) =1, and Cov(Y, Z) = 2. Determine (a) Var(X + Y + Z) (b) Var(3X Y 2Z + 1).

Q:

Statistics for three variables are given below. X is the monthly return for a large-stock index, Y is the monthly return for a small-stock index, and Z is the monthly return for a corporate bond...

Q:

For all random variables X, Y, and Z, let Cov(X, Y |z) denote the covariance ofX and Y in their conditional joint distribution given Z = z. Prove that Cov(X, Y) = E[Cov(X, Y |Z)] + Cov[E(X|Z),...

Q:

There are three categorical variables X, Y , and Z. If "X is marginally independent of Y ", is it true that "X is conditionally independent of Y "? If it is true, prove it. If it is not true, give a...

Q:

For three categorical variables A, B, and C: a. When C is jointly independent of A and B, show that A and C are conditionally independent, given B. b. Prove that mutual independence of A, B, and C...

Q:

Give a "real world" example of three variables X, Y, and Z, for which you expect X and Y to be marginally associated but conditionally independent, controlling for Z.

Q:

Give an example of three variables X, Y , and Z, for which you expect X and Y to be marginally associated but conditionally independent, controlling for Z.

Q:

Give a real world example of three variables X, Y , and Z, for which you expect X and Y to be marginally associated but conditionally independent, controlling for Z.

Q:

Exercises Chapter 2 2.1 Marginal and conditional probability: The social mobility data from Section 2.5 gives a joint probability distribution on (Y1 , Y2 )= (father's occupation, son's occupation)....

Q:

Algorithms in Artificial Intelligence (or, the old name: Introduction to Algorithmic Decision Making) Part 1 Based on slides by David Sarne and Lirong Xia Course Tentative Schedule Introduction...

Q:

A shareholder purchases 35% non controlling interest in a $80 million company. According to FASB statement no. 160, how would you reflect this on the balance sheet? If he or she sells 8% of the...

Q:

In 2002 a U.S. court of appeals imposed remedies relating to a lower court's findings that Microsoft had a monopoly in personal computer (PC) operating systems and had maintained its monopoly through...

Q:

A fall in tuition fees decreases a colleges total revenue if the price elasticity of demand for college education is a) negative. b) greater than zero but less than one. c) equal to one. d) greater...

Q:

2. If the earnings available on other financial assets rose, would you want to hold more or less money? Why?

Q:

Time magazine (July 15, 2002) quoted a poll of 10,000 Americans in which only 4% said they were vegetarians. a. What has to be assumed about this sample to construct a confidence interval for the...

Q:

When a GSS asked 1326 subjects, Do you believe in heaven? (coded HEAVEN), the proportion who answered yes was 0.85. From results in the next section, the estimated standard deviation of this point...

Q:

Consider the statement that it is better for the man to work and the woman to tend the home, from the GSS (variable denoted FEFAM). a. Go to the Web site, sda.berkeley.edu/GSS. Find the number who...

Q:

If two projects offer the same positive NPV, then they: also have the same IRR. have the same payback period. are mutually exclusive projects. add the same amount of value to the firm

Q:

Assume the Knight Corporation is considering the acquisition of Day Inc. The expected earnings per share for the Knight Corporation will be $8 with or without the merger. However, the standard...

Q:

Johnson Tire Distributors has an unlevered cost of capital of 12 percent, a tax rate of 34 percent, and expected earnings before interest and taxes of $1,900 in perpetuity. The company has $3,400 in...