variables X and Y. Using this information answer the questions below. Y=2 4c 2c X=1 X=2 That is, P(X = 1, Y = 1) = p(1, 1) = 1c and so forth. (a) Find the value of constant, c. (b) [Marginal distributions] Y=1 1c 3c i. Determine the probability mass functions (pmf) of X, px (x). ii. Find the cumulative distribution of X. iii. Find P(1.5 < X < 2). iv. Find P(1.5≤ x ≤ 2). (c) [Conditional distributions] (d) [Joint distribution] 1 i. Find conditional distribution of X given Y = 1, P(X = Y = 1), where z = 1,2. ii. Find the conditional expectation of X given Y = 1, E(X|Y = 1). iii. By using the law of iterated expectation (LIE), calculate E(X). A. Write down the expression for E(X) by using the law of iterated expectation (LIE). B. Calculate E(X). i. Calculate Cov(X,Y). ii. Calculate Cov(-2X,Y-4). iii. Calculate Var(X-2Y + 4).
variables X and Y. Using this information answer the questions below. Y=2 4c 2c X=1 X=2 That is, P(X = 1, Y = 1) = p(1, 1) = 1c and so forth. (a) Find the value of constant, c. (b) [Marginal distributions] Y=1 1c 3c i. Determine the probability mass functions (pmf) of X, px (x). ii. Find the cumulative distribution of X. iii. Find P(1.5 < X < 2). iv. Find P(1.5≤ x ≤ 2). (c) [Conditional distributions] (d) [Joint distribution] 1 i. Find conditional distribution of X given Y = 1, P(X = Y = 1), where z = 1,2. ii. Find the conditional expectation of X given Y = 1, E(X|Y = 1). iii. By using the law of iterated expectation (LIE), calculate E(X). A. Write down the expression for E(X) by using the law of iterated expectation (LIE). B. Calculate E(X). i. Calculate Cov(X,Y). ii. Calculate Cov(-2X,Y-4). iii. Calculate Var(X-2Y + 4).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![2. The following Table presents the joint probability distribution for two random
variables X and Y. Using this information answer the questions below.
X=1
X=2
Y=1
1c
3c
That is, P(X= 1, Y = 1) = p(1, 1) = 1c and so forth.
(a) Find the value of constant, c.
(b) [Marginal distributions]
iii. Find P(1.5 < X < 2).
iv. Find P(1.5 ≤ x ≤ 2).
(c) [Conditional distributions]
i. Determine the probability mass functions (pmf) of X, px (x).
ii. Find the cumulative distribution of X.
(d) [Joint distribution]
Y=2
4c
2c
1
i. Find conditional distribution of X given Y = 1, P(X = Y = 1),
where x = 1,2.
ii. Find the conditional expectation of X given Y = 1, E(X Y = 1).
iii. By using the law of iterated expectation (LIE), calculate E(X).
A. Write down the expression for E(X) by using the law of iterated
expectation (LIE).
B. Calculate E(X).
i. Calculate Cov(X,Y).
ii. Calculate Cov(-2X, Y-4).
iii. Calculate Var(X-2Y+4).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe875a456-3d0b-4a51-88f1-95129dcab190%2F2641a553-2259-4a04-bb1f-71ee87d6f0c9%2Fqzc4c08_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. The following Table presents the joint probability distribution for two random
variables X and Y. Using this information answer the questions below.
X=1
X=2
Y=1
1c
3c
That is, P(X= 1, Y = 1) = p(1, 1) = 1c and so forth.
(a) Find the value of constant, c.
(b) [Marginal distributions]
iii. Find P(1.5 < X < 2).
iv. Find P(1.5 ≤ x ≤ 2).
(c) [Conditional distributions]
i. Determine the probability mass functions (pmf) of X, px (x).
ii. Find the cumulative distribution of X.
(d) [Joint distribution]
Y=2
4c
2c
1
i. Find conditional distribution of X given Y = 1, P(X = Y = 1),
where x = 1,2.
ii. Find the conditional expectation of X given Y = 1, E(X Y = 1).
iii. By using the law of iterated expectation (LIE), calculate E(X).
A. Write down the expression for E(X) by using the law of iterated
expectation (LIE).
B. Calculate E(X).
i. Calculate Cov(X,Y).
ii. Calculate Cov(-2X, Y-4).
iii. Calculate Var(X-2Y+4).
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