Two discrete random variables X and Y are jointly distributed.
.1. Two discrete random variables X and Y are jointly distributed. The joint pmf is f(z, y) = 1/28 , SX = {0, 1, 2, 3, 4, 5,6}, and SY = {0, .... X), where Y is a non-negative integer
a) Find the marginal pdfs of X and Y
b) Caculate E(X) and E(Y).
2. Let the joint pdf of X aud Y be
a) Draw the graph of the support of X and Y
b) Determine c in the joint pdf.
c) Find E(X +Y), where x +Y ≤ 1.
Homework Answers
3. Let f(x,y) = xy-1 be the joint pmf/ pdf of two random variables X (discrete)...
3. Let f(x,y) = xy-1 be the joint pmf/ pdf of two random variables X (discrete) and Y (continuous), for x = 1, 2, 3, 4 and 0 <y < 2. (a) Determine the marginal pmf of X. (b) Determine the marginal pdf of Y. (c) Compute P(X<2 and Y < 1). (d) Explain why X and Y are dependent without computing Cou(X,Y).
1. Let X and Y be two jointly continuous random variables with joint CDF otherwsie a....
1. Let X and Y be two jointly continuous random variables with joint CDF otherwsie a. Find the joint pdf fxy(x, y), marginal pdf (fx(x) and fy()) and cdf (Fx(x) and Fy)) b. Find the conditional pdf fxiy Cr ly c. Find the probability P(X < Y = y) d. Are X and Y independent?
Suppose that X and Y are jointly continuous random variables with joint probability density function f(x,y)...
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.
Let X and Y be continuous random variables with joint pdf fx y (x, y)-3x, 0...
Let X and Y be continuous random variables with joint pdf fx y (x, y)-3x, 0 Sy and zero otherwise. 2. sx, a. What is the marginal pdf of X? b. What is the marginal pdf of Y? c. What is the expectation of X alone? d. What is the covariance of X and Y? e. What is the correlation of X and Y?
9. Suppose the discrete random variables X and Y are jointly distributed according to the following...
9. Suppose the discrete random variables X and Y are jointly distributed according to the following table: Y|Y -1 0 1 0.1 0.1 0.1 3 0 0.2 0.1 4. 0.2 0.1 0.1 1 a. Compute the expected values E(X) and E(Y), variances V(X) and V(Y), and covariance Cov(X,Y) of X and Y. [11] b. Let W = X – Y. Compute E(W) and V(W). [4]
-1 1 9. Suppose the discrete random variables X and Y are jointly distributed according to...
-1 1 9. Suppose the discrete random variables X and Y are jointly distributed according to the following table: 0 0.1 0.1 0.1 3 0 0.2 0.1 4 0.2 0.1 0.1 2x 1 a. Compute the expected values E(X) and E(Y), variances V(X) and V(Y), and covariance Cov(X,Y) of X and Y. [11] b. Let W = X – Y. Compute E(W) and V(W). [4]
Looking for help on question f and beyond 1. Suppose the discrete random variables X and...
Looking for help on question f and beyond
1. Suppose the discrete random variables X and Y have joint pmf (a) Find P(X < 1,Y 2 2) (b) Find P(Y-2) (c) Find P(x -Y) d) Find the marginal pmf of X, fx(x). Be sure to state the support (e) Find E(X) (f) Find the conditional pmf of Y given X- r, fy|x-»(b). Be sure to state the support (and the values a that can be conditioned on) (g) Find the...
The joint pdf of random variables X and Y is given by f(x.y)-k if 0 s...
The joint pdf of random variables X and Y is given by f(x.y)-k if 0 s y sx s 2 and f(x,y) =0 otherwise. a. Find the value of k b. Find the marginal pdfs of X and Y. Are X and Y independent? c. Find Covariance (X,Y) and Correlation(X,Y). Why cannot we say that X and Y have linear relation Y-a X+ b, where a and b are real numbers?
55. Let X and Y be jointly continuous random variables with joint density function fx.y(x,y) be-3y...
55. Let X and Y be jointly continuous random variables with joint density function fx.y(x,y) be-3y -a < x < 2a, 0) < y < 00, otherwise. Assume that E[XY] = 1/6. (a) Find a and b such that fx,y is a valid joint pdf. You may want to use the fact that du = 1. u 6. и е (b) Find the conditional pdf of X given Y = y where 0 <y < . (c) Find Cov(X,Y). (d)...
9. Suppose that the jointly distributed random variables X and Y have the following pdf (a)...
9. Suppose that the jointly distributed random variables X and Y have the following pdf (a) Find E(X +Y). (b) Find Cov(X, Y)
3. Let f(x,y) = xy-1 be the joint pmf/ pdf of two random variables X (discrete) and Y (continuous), for x = 1, 2, 3, 4 and 0 <y < 2. (a) Determine the marginal pmf of X. (b) Determine the marginal pdf of Y. (c) Compute P(X<2 and Y < 1). (d) Explain why X and Y are dependent without computing Cou(X,Y).
1. Let X and Y be two jointly continuous random variables with joint CDF otherwsie a. Find the joint pdf fxy(x, y), marginal pdf (fx(x) and fy()) and cdf (Fx(x) and Fy)) b. Find the conditional pdf fxiy Cr ly c. Find the probability P(X < Y = y) d. Are X and Y independent?
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.
Let X and Y be continuous random variables with joint pdf fx y (x, y)-3x, 0 Sy and zero otherwise. 2. sx, a. What is the marginal pdf of X? b. What is the marginal pdf of Y? c. What is the expectation of X alone? d. What is the covariance of X and Y? e. What is the correlation of X and Y?
9. Suppose the discrete random variables X and Y are jointly distributed according to the following table: Y|Y -1 0 1 0.1 0.1 0.1 3 0 0.2 0.1 4. 0.2 0.1 0.1 1 a. Compute the expected values E(X) and E(Y), variances V(X) and V(Y), and covariance Cov(X,Y) of X and Y. [11] b. Let W = X – Y. Compute E(W) and V(W). [4]
-1 1 9. Suppose the discrete random variables X and Y are jointly distributed according to the following table: 0 0.1 0.1 0.1 3 0 0.2 0.1 4 0.2 0.1 0.1 2x 1 a. Compute the expected values E(X) and E(Y), variances V(X) and V(Y), and covariance Cov(X,Y) of X and Y. [11] b. Let W = X – Y. Compute E(W) and V(W). [4]
Looking for help on question f and beyond
1. Suppose the discrete random variables X and Y have joint pmf (a) Find P(X < 1,Y 2 2) (b) Find P(Y-2) (c) Find P(x -Y) d) Find the marginal pmf of X, fx(x). Be sure to state the support (e) Find E(X) (f) Find the conditional pmf of Y given X- r, fy|x-»(b). Be sure to state the support (and the values a that can be conditioned on) (g) Find the...
The joint pdf of random variables X and Y is given by f(x.y)-k if 0 s y sx s 2 and f(x,y) =0 otherwise. a. Find the value of k b. Find the marginal pdfs of X and Y. Are X and Y independent? c. Find Covariance (X,Y) and Correlation(X,Y). Why cannot we say that X and Y have linear relation Y-a X+ b, where a and b are real numbers?
55. Let X and Y be jointly continuous random variables with joint density function fx.y(x,y) be-3y -a < x < 2a, 0) < y < 00, otherwise. Assume that E[XY] = 1/6. (a) Find a and b such that fx,y is a valid joint pdf. You may want to use the fact that du = 1. u 6. и е (b) Find the conditional pdf of X given Y = y where 0 <y < . (c) Find Cov(X,Y). (d)...
9. Suppose that the jointly distributed random variables X and Y have the following pdf (a) Find E(X +Y). (b) Find Cov(X, Y)
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