![81. Consider the function g(x, y) given by, 1 1.52.53 11/4 0 0 0 2 0 1/8 0 0 y 3 0 1/4 0 0 4 0 0 1/4 0 5 00 0 1/8 and complete / determine the following: (a) Show that g(x, y) satisfies the properties of a joint pmf. (See Table in ?6.0.1.) (b) P(X < 2.5,Y < 3) (c) P(X < 2.5) (d) P(Y < 3) (e) P(X> 1.8, Y> 4.7) (f) E[X], EY], Var(X), Var(Y) (g) Marginal probability distribution of X (h) Conditional probability distribution of Y given that X - 1.5 (i) Conditional probability distribution of X given that Y -2 (G) EY |X -1.5] (k) Are X and Y independent?](http://img.homeworklib.com/questions/59ad2bd0-56b7-11ec-bb87-8dc643b7d789.png?x-oss-process=image/resize,w_560)
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81. Consider the function g(x, y) given by, 1 1.52.53 11/4 0 0 0 2 0...
Consider joint probability distribution given below y fxy (x, у) х 1.0 1 11/32 1/32 1.5...
Consider joint probability distribution given below y fxy (x, у) х 1.0 1 11/32 1/32 1.5 2 1.5 1/4 2.5 4 1/4 3.0 1/8 Determine the following: In your intermediate calculations, round all fractions to three decimal places. Round your answers to three decimal places (e.g 98.765) (a) Conditional probability distribution of Y qiven that X = 1,5. у Fуus 0) 1 2 3 5 (b) Conditional probability distribution of X given that Y 2. 1.0 1.5 2.5 (c) E(YIX...
Exercises: 1) The joint distribution of X and Y is given by the following table: y...
Exercises: 1) The joint distribution of X and Y is given by the following table: y 1.5 2 fxy(x, y) 1/4 1/8 1/4 1/4 1/8 Compute: a) P(X=1.5, Y =2). b) P(X=1, Y =2). c) P(X=1.5). d) P(X<2.5, Y<3) e) P(Y>3) f) E(X), E(Y), V(X) and V(Y). g) The marginal distributions of X and of Y. h) Conditional probability distribution of Y given that X = 1.5. i) E(Y|X=1.5) j) E(XY) k) Are X and Y independent? Explain why or...
1. Let the joint probability (mass) function of X and Y be given by the following:...
1. Let the joint probability (mass) function of X and Y be given by the following: Value of X -1 -1 3/8 1/8 Value of Y1 1/8 3/8 (a) Determine the marginal (b) Determine the conditional distribution of X given Y (c) Are they independent? d) Compute E(X), Var(X), E(Y) and Var(Y). (e) Compute PXY <0) and Ptmax(X,Y) > 0 (f) Compute Elmax(X, Y)] and E(XY) (g) Compute Cov(X,Y) and Corr(X, Y) 1
Consider fx (x)=e*, 0<x and joint probability density function fx (x, y) = e) for 0<x<y....
Consider fx (x)=e*, 0<x and joint probability density function fx (x, y) = e) for 0<x<y. Determine the following: (a) Conditional probability distribution of Y given X =1. (b) ECY X = 1) = (c) P(Y <2 X = 1) = (d) Conditional probability distribution of X given Y = 4.
1. Suppose you have two random variables, X and Y with joint distribution given by the...
1. Suppose you have two random variables, X and Y with joint distribution given by the following tables So, for example, the probability that Y o,x - 0 is 4, and the probability that Y (a) Find the marginal distributions (pmfs) of X and Y, denoted f(x),J(Y). (b) Find the conditional distribution (pmf) of Y give X, denoted f(YX). (c) Find the expected values of X and Y, EX), E(Y). (d) Find the variances of X and Y, Var(X),Var(Y). (e)...
you have two random variables, X and Y with joint distribution given by the following table:...
you have two random variables, X and Y with joint distribution given by the following table: Y=0 | .4 .2 4+.26. So, for example, the probability that Y 0, X - 0 is 4, and the probability that Y (a) Find the marginal distributions (pmfs) of X and Y, denoted f(x),f(r). (b) Find the conditional distribution (pmf) of Y give X, denoted f(Y|X). (c) Find the expected values of X and Y, E(X), E(Y). (d) Find the variances of X...
2. The joint pmf of X and Y is given below. f(x,y) 0 1 2 Y...
2. The joint pmf of X and Y is given below. f(x,y) 0 1 2 Y 0 1/10 3/100 1 3/10 2/10 1/10 a. Compute P(Y = 0|1 < X < 2). b. Compute E(X|Y = y) for y = 0,1. C. Evaluate Ey[E(X|Y)] using the formula Ey [E(X|Y)] = {y E(X|Y = y) f (y) and the results of part (b). d. Evaluate E(X) using the formula E(X) = Exxfx(x). Note that your answers in (c) and (d) should...
1. Consider the joint probability density function 0<x<y, 0<y<1, fx.x(x, y) = 0, otherwise. (a) Find...
1. Consider the joint probability density function 0<x<y, 0<y<1, fx.x(x, y) = 0, otherwise. (a) Find the marginal probability density function of Y and identify its distribution. (5 marks (b) Find the conditional probability density function of X given Y=y and hence find the mean and variance of X conditional on Y=y. [7 marks] (c) Use iterated expectation to find the expected value of X [5 marks (d) Use E(XY) and var(XY) from (b) above to find the variance of...
6. (20%) Consider two random variables X and Y with the joint PMF given in Table...
6. (20%) Consider two random variables X and Y with the joint PMF given in Table 2. Table 2: Joint PMF of X and Y Y =0Y 1 X 0 X 1 0 (a) (5%) Find the PMF of X and PMF of Y. (b) (5%) Find EX, EY, Var(X), Var(Y (c) (10%)Find the MMSE estimator of X given Y, (M) for both Y 0 and Y 1
Determine the value of such that the function f (x, y) = cxy for 0<x<3 and...
Determine the value of such that the function f (x, y) = cxy for 0<x<3 and 0 <y<3 satisfies the properties of a joint probability density function. Determine the following. Round your answers to four decimal places (e.g. 98.7654). 1.0994 P&<2,Y<3) 7.4444 P(X<2.0) 21:1878 Pu<Y<1,7) 12489 P(X>1.8,1 <Y<2.5) 7:3733 EX) P(X < 0,8< 4)
Consider joint probability distribution given below y fxy (x, у) х 1.0 1 11/32 1/32 1.5 2 1.5 1/4 2.5 4 1/4 3.0 1/8 Determine the following: In your intermediate calculations, round all fractions to three decimal places. Round your answers to three decimal places (e.g 98.765) (a) Conditional probability distribution of Y qiven that X = 1,5. у Fуus 0) 1 2 3 5 (b) Conditional probability distribution of X given that Y 2. 1.0 1.5 2.5 (c) E(YIX...
Exercises: 1) The joint distribution of X and Y is given by the following table: y 1.5 2 fxy(x, y) 1/4 1/8 1/4 1/4 1/8 Compute: a) P(X=1.5, Y =2). b) P(X=1, Y =2). c) P(X=1.5). d) P(X<2.5, Y<3) e) P(Y>3) f) E(X), E(Y), V(X) and V(Y). g) The marginal distributions of X and of Y. h) Conditional probability distribution of Y given that X = 1.5. i) E(Y|X=1.5) j) E(XY) k) Are X and Y independent? Explain why or...
1. Let the joint probability (mass) function of X and Y be given by the following: Value of X -1 -1 3/8 1/8 Value of Y1 1/8 3/8 (a) Determine the marginal (b) Determine the conditional distribution of X given Y (c) Are they independent? d) Compute E(X), Var(X), E(Y) and Var(Y). (e) Compute PXY <0) and Ptmax(X,Y) > 0 (f) Compute Elmax(X, Y)] and E(XY) (g) Compute Cov(X,Y) and Corr(X, Y) 1
Consider fx (x)=e*, 0<x and joint probability density function fx (x, y) = e) for 0<x<y. Determine the following: (a) Conditional probability distribution of Y given X =1. (b) ECY X = 1) = (c) P(Y <2 X = 1) = (d) Conditional probability distribution of X given Y = 4.
1. Suppose you have two random variables, X and Y with joint distribution given by the following tables So, for example, the probability that Y o,x - 0 is 4, and the probability that Y (a) Find the marginal distributions (pmfs) of X and Y, denoted f(x),J(Y). (b) Find the conditional distribution (pmf) of Y give X, denoted f(YX). (c) Find the expected values of X and Y, EX), E(Y). (d) Find the variances of X and Y, Var(X),Var(Y). (e)...
you have two random variables, X and Y with joint distribution given by the following table: Y=0 | .4 .2 4+.26. So, for example, the probability that Y 0, X - 0 is 4, and the probability that Y (a) Find the marginal distributions (pmfs) of X and Y, denoted f(x),f(r). (b) Find the conditional distribution (pmf) of Y give X, denoted f(Y|X). (c) Find the expected values of X and Y, E(X), E(Y). (d) Find the variances of X...
2. The joint pmf of X and Y is given below. f(x,y) 0 1 2 Y 0 1/10 3/100 1 3/10 2/10 1/10 a. Compute P(Y = 0|1 < X < 2). b. Compute E(X|Y = y) for y = 0,1. C. Evaluate Ey[E(X|Y)] using the formula Ey [E(X|Y)] = {y E(X|Y = y) f (y) and the results of part (b). d. Evaluate E(X) using the formula E(X) = Exxfx(x). Note that your answers in (c) and (d) should...
1. Consider the joint probability density function 0<x<y, 0<y<1, fx.x(x, y) = 0, otherwise. (a) Find the marginal probability density function of Y and identify its distribution. (5 marks (b) Find the conditional probability density function of X given Y=y and hence find the mean and variance of X conditional on Y=y. [7 marks] (c) Use iterated expectation to find the expected value of X [5 marks (d) Use E(XY) and var(XY) from (b) above to find the variance of...
6. (20%) Consider two random variables X and Y with the joint PMF given in Table 2. Table 2: Joint PMF of X and Y Y =0Y 1 X 0 X 1 0 (a) (5%) Find the PMF of X and PMF of Y. (b) (5%) Find EX, EY, Var(X), Var(Y (c) (10%)Find the MMSE estimator of X given Y, (M) for both Y 0 and Y 1
Determine the value of such that the function f (x, y) = cxy for 0<x<3 and 0 <y<3 satisfies the properties of a joint probability density function. Determine the following. Round your answers to four decimal places (e.g. 98.7654). 1.0994 P&<2,Y<3) 7.4444 P(X<2.0) 21:1878 Pu<Y<1,7) 12489 P(X>1.8,1 <Y<2.5) 7:3733 EX) P(X < 0,8< 4)
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