Suppose that X and Y are conditionally independent, given Z, and X and Z are marginally independent.

Question:

a. Show that X is jointly independent of Y and Z.

b. Show X and Y are marginally independent.

c. Show that if X and Z are conditionally (rather than marginally) independent, then X and Y are still marginally independent.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Categorical Data Analysis

ISBN: 9780471360933

2nd Edition

Authors: Alan Agresti

See More Books

Question Posted: Feb 14, 2020 06:25 AM

See More Questions

Suppose that X and Y are i.i.d. random variables, and that each has the following p.d.f.: Also, let U = X/(X + Y) and V = X + Y. a. Determine the joint p.d.f. of U and V. b. Are U and V independent?...
Suppose that X and Y are independent random variables for which Var(X) = Var(Y) = 3. Find the values of (a) Var(X Y) (b) Var(2X 3Y + 1).
Suppose that X and Y are random variables for which E(X) = 3, E(Y) = 1, Var(X) = 4, and Var(Y) = 9. Let Z = 5X Y + 15. Find E(Z) and Var(Z) under each of the following conditions: (a) X and Y are...
Write a Summary of Tartuffe the Norton anthology of western literature.
Canal+France, a subsidiary of Vivendi, acquired 85 percent of TPS Cinema in January 2007 for 787 millionfair value of Canal+France shares. Information on the acquisition is as follows (in millions):...
Advances in research and development in the pharmaceutical industry have enabled manufacturers to identify potential cures more quickly and therefore at lower cost. At the same time, the aging of our...
On June 8, 2017, Eugene Weiner made a post on Isaac Aflalos Facebook page. The post read, Yurim and Isaac took advantage of a old 94plus sick man elder abuse [sic]. Alflalo took umbrage to the post...
Burke Corporation was organized on January 1, 2014. It is authorized to issue 10,000 shares of 8%, $100 par value preferred stock, and 500,000 shares of no-par common stock with a stated value of $2...
Let U={1,2,3,...,10}, A={1,3,5,7}, B={1,2,3,4}, and C={3,4,6,7,9}. Find BC'
The previous year was Amys first year of operating the bookstore. Amy and Ken elected to carry forward a $4,752 net operating loss from the first year of business into 2015. (Note: Net operating...
Standardize Table 10.6. Describe the migration patterns. Table 10.6: Migration from 1980 to 1985, with Fit of Marginal Homogeneity Model Residence in 1985 Residence in 1980 Northeast Midwest South...
Suppose that model (XY, XZ, YZ) holds in a 2 X 2 X 2 table, and the common XY conditional Log odds ratio at the two levels of Z is positive. If the XZ and YZ conditional log odds ratios are both...
A tank full of water has the shape of a paraboloid of revolution as shown in the figure; that is, its shape is obtained by rotating a parabola about a vertical axis. (a) If its height is 4 ft and the...
Integrate real-world examples of how social media presence in law enforcement organizations was helpful to the agency. In other words, what are the positive aspects of law enforcement using social...
In today's generation, social media has a large impact on society. Discuss the three factors that should be considered during the process of social media management. Secondly, do you believe law...
Why is growing the number of users such an important metric for social media companies? How does Metcalfe's Law relate to the profitability of social media companies?
There is much misinformation about COVID vaccines being disseminated on Facebook and other social media. Assume Congress passed a law prohibiting Facebook and other social media platforms from...
In a common law legal system, only governments can create a Statutory Law. In relation to the media, what would be a media policy? Or What is the major difference between a policy and a law with...
Darcy borrowed $4,000 in 2013 from her employer to purchase a new computer. She repays $1,000 of the loan plus 6% interest on the unpaid balance in 2013, 2014, and 2015. After closing a big deal in...
Cobb Manufacturing Company uses a process cost system and average costing. The following production data is for the month of June 2011. Production Costs Work in process, beginning of the month:...
Refer to the previous exercise. a. Would the results of your analysis change if for the second Bumper A the repair cost was $9000 instead of $2500? What does this illustrate about the analysis? b....
In Exercise 15.8, the telephone holding times for Muzak and classical music were Muzak 0, 1, 4, 6, 3 Classical 13, 9, 8, 15, 7 a. For comparing these two groups with the Wilcoxon test, report the...
Refer to the previous exercise. For the actual experiment, suppose the participants using the tanning studio got ranks 1 and 2 and the participants using the tanning lotion got ranks 3 and 4. a. Find...
8 (a) Find a function that represents the power series 3 (k + 1) x *. As always, show all work. [Hint: Split it.] k=0 (b) Use your answer from (a) to find the sum of the series answer as a reduced...
The function f(x)=2x^(4)+x^(3)-7x^(2)+4 has at least two rational roots. Use the rational root theorem to find those roots, then proceed to find all complex roots. (Note: roots may be integer,...
Wildcat Company is considering a 5-for-3 stock split. The current price is $57.00 per share, and Wildcat believes that its total market value would increase by 7.5% as a result of the improved...

Suppose that X and Y are conditionally independent, given Z, and X and Z are marginally independent.

Question:

Step by Step Answer:

Solution a Show that X is conditionally independent of Y given Z by considering the case where Z equ...View the full answer

Categorical Data Analysis

Students also viewed these Mathematics questions