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. Suppose that the joint probability mass function of X and Y is e probability mass...
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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...
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].
Suppose that X and Y are jointly continuous random variables with joint probability density function f(x,y) = {12rºy, 1 0, 0<x<a, 0<y<1 otherwise i) Determine the constant a ii) Find P(0<x<0.5, O Y<0.25) HE) Find the marginal PDFs fex) and y) iv) Find the expected value of X and Y. Le. E(X) and E(Y) v) Are X and Y independent? Justify your answer.
7. Let X and Y have joint probability mass function fx.y(x,y) = (x+y)/30 for x = 0.1, 2.3 and y0,1,2. Find (a) PrX 2,Y-1) (b) PrX>2,Y S1) (c) Pr(X + Y=4) (d) Pr[X >Y) (e) the marginal probability mass function of Y, and (f) E[XY]
Problem #8: Suppose that X and Y have the following joint probability density function. f(x,y)- ^x, 0 < x < 5, y> 0, x-2 <y <x+:2 146 (a) Find E(XY (b) Find the covariance between X and Y. Problem #8: Suppose that X and Y have the following joint probability density function. f(x,y)- ^x, 0
7. Let X and Y have joint probability mass function fx,y(x,y) = (z+y)/30 for x = 0, 1, 2, 3 and y-0,1,2. Find (a) Pr(X 2, Y=1} (b) PríX > 2, Y 1) (c) PrXY-4) (d) PrX>Y. (e) the marginal probability mass function of Y, and (f) E[XY]
5. Random variables X and Y have joint probability mass function otherwise (a) Find the value of the constant c. (b) Find and sketch the marginal probability mass function Py (u). (c) Find and sketch the marginal probability mass function Px (rk). (d) Find P(Y <X). (e) Find P(Y X) (g) Are X and Y independent? 2 内?
Q.4 (22') Suppose the joint probability density function of X and Y is fx,y(x, y) = { „) - k(2 - x + y)x 0 sxs 1,0 sys1 o otherwise (a) (7”) Show that the value of constant k = 12 (b) (7') Find the marginal density function of X, i.e., fx(x). (c) (8') Find the conditional probability density of X given Y=y, i.e., fxy(xly). 11
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...