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3. Consider the following joint probability mass functiono Py (y) 0 0.10 0.20 Y 1 0.10...
(20 points) Consider the following joint distribution of X and Y ㄨㄧㄚ 0 0.1 0.2 1 0.3 0.4 (a) Find the marginal distributions of X and Y. (i.e., Px(x) and Py()) (b) Find the conditional distributio...
(20 points) Consider the following joint distribution of X and Y ㄨㄧㄚ 0 0.1 0.2 1 0.3 0.4 (a) Find the marginal distributions of X and Y. (i.e., Px(x) and Py()) (b) Find the conditional distribution of X given Y-0. (i.e., Pxjy (xY-0)) (c) Compute EXIY-01 and Var(X)Y = 0). (d) Find the covariance between X and Y. (i.e., Cov(X, Y)) (e) Are X and Y independent? Justify your answer.
(20 points) Consider the following joint distribution of X and...
1. Suppose X and Y are discrete random variables with joint probability mass function fxy defined...
1. Suppose X and Y are discrete random variables with joint probability mass function fxy defined by the following table: 3 y fxy(x, y) 01 3/20 02 10 7/80 3/80 1/5 1/16 3/20 3/16 1/8 2 3 2 3 a Find the marginal probability mass function for X. b Find the marginal probability mass function for Y. c Find E(X), EY],V (X), and V (Y). d Find the covariance between X and Y. e Find the correlation between X and...
4.23 Suppose that X and Y have the following joint probability function: 1 0.10 0.15 y|...
4.23 Suppose that X and Y have the following joint probability function: 1 0.10 0.15 y| 3 | 0.20 0.30 5 0.10 0.15 (a) Find the expected value of g(x, Y) XY2 (b) Find μχ and μΥ.
0 Consider the discrete random variables X and Y with the following joint probability mass function:...
0 Consider the discrete random variables X and Y with the following joint probability mass function: . -1 1/8 0 1/4 0 1 1/4 1/8 -1 1 1/8 1/8 What is P(X = 1 Y = 0)? Are X and Y independent? 0 A. 0; independent B. 1/2; independent C. 1/2; dependent D. 1/8: dependent E. none of the preceding
Please show how did you came up with the answer, show formulas and work. Also, please do Parts e to i. Thank you so much 1. Consider the following probability mass function for the discrete joint pro...
Please show how did you came up with the answer, show formulas
and work. Also, please do Parts e to i. Thank you so much
1. Consider the following probability mass function for the discrete joint probability distribution for random variables X and Y where the possible values for X are 0, 1, 2, and 3; and the possible values for Y are 0, 1, 2, 3, and 4. p(x,y) <0 3 0 4 0.01 0 0 0.10 0.05 0.15...
The following table presents the joint probability mass function pmf of variables X and Y 0...
The following table presents the joint probability mass function pmf of variables X and Y 0 2 0.14 0.06 0.21 2 0.09 0.35 0.15 (a) Compute the probability that P(X +Y 3 2) (b) Compute the expected value of the function (X, Y)3 (c) Compute the marginal probability distributions of X and )Y (d) Compute the variances of X and Y (e) Compute the covariance and correlation of X and Y. (f) Are X and Y statistically independent? Clearly prove...
Let X and Y have joint probability mass function fX,Y (x, y) = (x + y)/30...
Let X and Y have joint probability mass function fX,Y (x, y) = (x + y)/30 for x = 0, 1, 2, 3 and y = 0,1,2. Find: (a) Pr{X ≤ 2, Y = 1}(b) Pr{X > 2, Y ≤ 1} (c) Pr{X +Y = 4}. (d) Pr{X > Y }. (e) the marginal probability mass function of Y , and (f) E[XY].
Consider the discrete random variables X and Y with the following joint probability mass function: 2...
Consider the discrete random variables X and Y with the following joint probability mass function: 2 y fxy(x,y) -1 0 1/8 0 -1 1/4 0 1/4 0 1/8 -1 1/8 1 -1 1/8 What is P(X = 1 Y = 0)? Are X and Y independent? 1 1 1 A. 0; independent B. 1/2; independent C. 1/2; dependent D. 1/8; dependent E. none of the preceding 3. Multiple Choice Question Suppose that the number of bad cheques received by a...
(d) Find the probability mass function of X given Y = 3 (ie, p(x|y = 3))...
(d) Find the probability mass function of X given Y = 3 (ie,
p(x|y = 3))
7. (10 points) Consider two jars, Jar M and Jar W. In Jar M, there are 3 balls numbered 0, 1, 2. In Jar W there are 3 balls numbered 1, 2, 3. A ball is drawn from Jar M, then a ball is drawn from Jar W. Define M as the number on the ball from Jar A and W the number on...
(20 points) Consider the following joint distribution of X and Y ㄨㄧㄚ 0 0.1 0.2 1 0.3 0.4 (a) Find the marginal distributions of X and Y. (i.e., Px(x) and Py()) (b) Find the conditional distribution of X given Y-0. (i.e., Pxjy (xY-0)) (c) Compute EXIY-01 and Var(X)Y = 0). (d) Find the covariance between X and Y. (i.e., Cov(X, Y)) (e) Are X and Y independent? Justify your answer.
(20 points) Consider the following joint distribution of X and...
1. Suppose X and Y are discrete random variables with joint probability mass function fxy defined by the following table: 3 y fxy(x, y) 01 3/20 02 10 7/80 3/80 1/5 1/16 3/20 3/16 1/8 2 3 2 3 a Find the marginal probability mass function for X. b Find the marginal probability mass function for Y. c Find E(X), EY],V (X), and V (Y). d Find the covariance between X and Y. e Find the correlation between X and...
4.23 Suppose that X and Y have the following joint probability function: 1 0.10 0.15 y| 3 | 0.20 0.30 5 0.10 0.15 (a) Find the expected value of g(x, Y) XY2 (b) Find μχ and μΥ.
0 Consider the discrete random variables X and Y with the following joint probability mass function: . -1 1/8 0 1/4 0 1 1/4 1/8 -1 1 1/8 1/8 What is P(X = 1 Y = 0)? Are X and Y independent? 0 A. 0; independent B. 1/2; independent C. 1/2; dependent D. 1/8: dependent E. none of the preceding
Please show how did you came up with the answer, show formulas
and work. Also, please do Parts e to i. Thank you so much
1. Consider the following probability mass function for the discrete joint probability distribution for random variables X and Y where the possible values for X are 0, 1, 2, and 3; and the possible values for Y are 0, 1, 2, 3, and 4. p(x,y) <0 3 0 4 0.01 0 0 0.10 0.05 0.15...
The following table presents the joint probability mass function pmf of variables X and Y 0 2 0.14 0.06 0.21 2 0.09 0.35 0.15 (a) Compute the probability that P(X +Y 3 2) (b) Compute the expected value of the function (X, Y)3 (c) Compute the marginal probability distributions of X and )Y (d) Compute the variances of X and Y (e) Compute the covariance and correlation of X and Y. (f) Are X and Y statistically independent? Clearly prove...
Consider the discrete random variables X and Y with the following joint probability mass function: 2 y fxy(x,y) -1 0 1/8 0 -1 1/4 0 1/4 0 1/8 -1 1/8 1 -1 1/8 What is P(X = 1 Y = 0)? Are X and Y independent? 1 1 1 A. 0; independent B. 1/2; independent C. 1/2; dependent D. 1/8; dependent E. none of the preceding 3. Multiple Choice Question Suppose that the number of bad cheques received by a...
(d) Find the probability mass function of X given Y = 3 (ie,
p(x|y = 3))
7. (10 points) Consider two jars, Jar M and Jar W. In Jar M, there are 3 balls numbered 0, 1, 2. In Jar W there are 3 balls numbered 1, 2, 3. A ball is drawn from Jar M, then a ball is drawn from Jar W. Define M as the number on the ball from Jar A and W the number on...
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