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1) Given the following table representing the joint probability distribution of the discrete Random variable (X, Y) X 1 2 3 1/12 0 2 1/6 1/9 1/18 1/4 3 0 1/5 2/15 a) Evaluate the marginal distribution of X and Y. b) Find the conditional distribution of X given Y = 2. c) Find the conditional distribution of Y given X= 3.

1) Given the following table representing the joint probability distribution of the discrete Random variable (X, Y) X 1 2 3 1/12 0 2 1/6 1/9 1/18 1/4 3 0 1/5 2/15 a) Evaluate the marginal distribution of X and Y. b) Find the conditional distribution of X given Y = 2. c) Find the conditional distribution of Y given X= 3.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Instruction: Work out the following questions by showing all necessary steps 1) Given the following table representing the joint probability distribution of the discrete Random variable (X, Y) X 1 3 X 1 0 P(x) 0 Then, evaluate 1/12 0 1/18 2 = 1/6 1/9 1 k 1/4 a) Evaluate the marginal distribution of X and Y b) Find the conditional distribution of X given Y = 2. c) Find the conditional distribution of Y given X= 3. d) Find the covariance b/n X and Y e) Calculate the correlation coefficient b/n X and Y 2) A random variable X has the following probability mass function. a) Value of k b) E (2x+5) c) V (3X+2) ||| 3 0 2 1/5 2k 2/15 3 2k ✓ What are the advantages of sampling? ✓ What are the limitations of sampling? 1 4 3k 3) Suppose that 4% of all TVs made by A&B Company in 2000 are defective. If eight of these TVs are randomly selected from across the country and tested, what is the probability that exactly three of them are defective? Assume that each TV is made independently of the others. 4) Prepare a document on sampling which answers all the following questions ✓ What is sampling in research and its methods? ✓ How do you describe a sample? ✓ What are the 5 basic sampling methods? ✓ What are the 4 sampling strategies? ✓ What are the 4 types of sampling? ✓Briefly explain all of them using examples ✓ What are the steps in sampling process? ✓ What are the principles of sampling? 5 K² ✓ What is the scope of sampling? ✓ What are some problems with the sampling technique? Do not forget to include brief and clear examples for each sampling technique O 6 2K² 7 7 K²+k <
Transcribed Image Text:Instruction: Work out the following questions by showing all necessary steps 1) Given the following table representing the joint probability distribution of the discrete Random variable (X, Y) X 1 3 X 1 0 P(x) 0 Then, evaluate 1/12 0 1/18 2 = 1/6 1/9 1 k 1/4 a) Evaluate the marginal distribution of X and Y b) Find the conditional distribution of X given Y = 2. c) Find the conditional distribution of Y given X= 3. d) Find the covariance b/n X and Y e) Calculate the correlation coefficient b/n X and Y 2) A random variable X has the following probability mass function. a) Value of k b) E (2x+5) c) V (3X+2) ||| 3 0 2 1/5 2k 2/15 3 2k ✓ What are the advantages of sampling? ✓ What are the limitations of sampling? 1 4 3k 3) Suppose that 4% of all TVs made by A&B Company in 2000 are defective. If eight of these TVs are randomly selected from across the country and tested, what is the probability that exactly three of them are defective? Assume that each TV is made independently of the others. 4) Prepare a document on sampling which answers all the following questions ✓ What is sampling in research and its methods? ✓ How do you describe a sample? ✓ What are the 5 basic sampling methods? ✓ What are the 4 sampling strategies? ✓ What are the 4 types of sampling? ✓Briefly explain all of them using examples ✓ What are the steps in sampling process? ✓ What are the principles of sampling? 5 K² ✓ What is the scope of sampling? ✓ What are some problems with the sampling technique? Do not forget to include brief and clear examples for each sampling technique O 6 2K² 7 7 K²+k <
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