Question: 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

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 implies that A and B are (i)

marginally independent and (ii) conditionally independent, given C.

c. Suppose that A is independent of B and that B is independent of C. Does this imply that A is independent of C? Explain.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock 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 Linear State Space Systems Questions!

Q:

____________________________________________________________________________________ BUSI 410 FINAL EXAM - Fall 2013 The regular exam length is 3 hours. This exam consists of three short cases: Case...

Q:

ANSI-SPARC6 Programming Language Compilation Write notes on each of the following topics: (a) the implementation of labels and jumps in a recursive, block structured programming language [7 marks]...

Q:

Suppose that X and Y are two independent continuous random variables with finite variances. Show that Var(Y|X = x) does not depend on x R. [4] (b) Now let Y = AX + BX3, where the three random...

Q:

- A. B. C. D. E. F. G. H. I. J. K. L. M. Contingency tables - A. B. C. D. E. F. G. H. I. J. K. L. M. a contingency table shows ___ - A. B. C. D. E. F. G. H. I. J. K. L. M. Contingency table a tool to...

Q:

Practice assignment id like to get done in the next 24 hours! Thanks :) 1). Suppose the following information is collected at a fast-food restaurant. Classify each of these variables as categorical...

Q:

bus230 please read first the research then answer the tasks the questions are the last 2 papers (2007), Koohsar.et al (2007) showed that there is no significant relation between emotional...

Q:

Mary is conducting research on Covid-19 and its possible symptoms. The study consists of 3 random variables: A, B and C, which are defined as follows: 1. A: Loss of smell 2. B: Presence of Covid -19...

Q:

Mary is conducting research on Covid-19 and its possible symptoms. The study consists of 3 random variables: A, B and C, which are defined as follows: 1. A: Loss of smell 2. B: Presence of Covid -19...

Q:

E-Tutorial Physics Book Note: I have attached below the lesson for the two (2) activities. Thank you. Activity 1. Directions: Look at each circuit below and show the solution using Kirchhoff's Rules...

Q:

1. a) Consider two clusters A and B each hosting multiple applications. All applications send bursty traffic between A and B over a link E. Under what conditions is circuit switching more efficient...

Q:

Exactly 10 years ago, Boyditch Professional Associates purchased $100,000 in depreciable assets with an estimated salvage of $10,000. For tax depreciation, the SL method with n = 10 years was used,...

Q:

What is the attorney-client privilege and what is the rationale for its existence?

Q:

14 Here are three formula cards. b= 18 a c-bx(2-1)-3(-11) a Work out the value of d when Explain the method you used. 23 = Work out the value of d when a= Explain the method you used.

Q:

Evaluate the integral. tan 3 d

Q:

Read about the first Physicians Health Study at phs.bwh.harvard.edu. a. Explain whether it was (i) an experiment or an observational study and (ii) a retrospective or prospective study. b. Identify...

Q:

During the 1980s approximately 22,000 physicians over the age of 40 agreed to participate in a long-term study called the Physicians Health Study. One question investigated was whether aspirin helps...

Q:

Refer to Exercise 4.71. One potential confounding variable was the amount of exercise the physicians got. The randomization should have balanced the treatment groups on exercise. The contingency...

Q:

3 The trial balance of Akintola failed to agree, the difference of N23.000 way of the suspensa account. The following errors we detect vi) A sum of N25.000 representing credit sules to a customer was...

Q:

47 7 A fx 331000 B D E F ? B Add: Finance from bank 170,000.00 10,000.00 ? ? 9 Less: Payment to bank 0 Less: Payment of interest - bank loan (5,300.00) ? 01 Net Closing Cash Balance $ 50,000.00 ? ? $...

Q:

Assume a $72,000 investment and the following cash flows for two alternatives Year 1 2 Investment X Investment Y $22,000 $22,000 20,000 20,000 15,000 40,000 10,000 30,000 Calculate the payback period...