Given the joint probability table blow,Fill the empty cells. Find the marginal probabilities of given X...
Given the following joint distribution of two random variables X and Y (a) Compute marginal distribution PX(x) (b) Compute marginal distribution PY(y) (c) What is the conditional probability P(Y | X = 2)? 20.10 0.05 0.15 0.10 0.10 4 0.04 0.02 0.06 0.04 0.04 6 0.04 0.02 0.06 0.06 0.02 8 0.02 0.01 0.03 0 0.04
Let X and Y be jointly continuous random variables with joint probability density given by f(x, y) = 12/5(2x − x2 − xy) for 0 < x < 1, 0 < y < 1 0 otherwise (a) Find the marginal densities for X and Y . (b) Find the conditional density for X given Y = y and the conditional density for Y given X = x. (c) Compute the probability P(1/2 < X < 1|Y =1/4). (d) Determine whether...
Let X and Y be jointly continuous random variables with joint probability density given by f(x, y) = 12/5(2x − x2 − xy) for 0 < x < 1, 0 < y < 1 0 otherwise (a) Find the marginal densities for X and Y . (b) Find the conditional density for X given Y = y and the conditional density for Y given X = x. (c) Compute the probability P(1/2 < X < 1|Y =1/4). (d) Determine whether...
2. Given k(2x + 3y) if a_ 0.1.2: у-0, 1. plx,y) - is a joint probability mass function(discrete case). a. What is k? b. Find the momen generating function Mx(t) c. Find the conditional probabilities P(Y X), P(Y 0X 1), P(X 1Y 0 2. Given k(2x + 3y) if a_ 0.1.2: у-0, 1. plx,y) - is a joint probability mass function(discrete case). a. What is k? b. Find the momen generating function Mx(t) c. Find the conditional probabilities P(Y X),...
(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...
Consider the following joint probability distribution on the random variables X and Y given in matrix form by Pxy P11 P12 P13 PXY-IP21 p22 p23 P31 P32 P33 P41 P42 P43 HereP(i, j) P(X = z n Y-J)-Pu represents the probability that X-1 and Y = j So for example, in the previous problem, X and Y represented the random variables for the color ([Black, Red]) and utensil type (Pencil,Pe pblackpen P(X = Black Y = Pen) = P(Black n...
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?
Suppose that the following table is the joint probability distribution of two random variables X and Y: х -2 0 2 3 0.27 0.08 0.16 0.2 0.1 0.04 0.1 0.05 a. Find the marginal PDF of X when x=-2, 0, 2, and 3. b. Find the marginal PDF of Y when y=2 and 5. . Find the conditional PDF of x=-2 and 3 given that y=2 has occurred. . Find the conditional PDF of y=2 and 5 given that x=3...
The joint probability density function for continuous random variables X and Y is given below. f (x) = x + y, 0 < x < 1, 0 < y < 1 if; 0, degilse. (a) Show that this is a joint density function. (b) Find the marginal density of X . (c) Find the marginal density of Y . (d) Given Y = y find the conditional density of X . (e) P ( 1/2 < X < 1|Y =...
The joint probability density function for continuous random variables X and Y is given below. f (x) = x + y, 0 < x < 1, 0 < y < 1 if; 0, degilse. (a) Show that this is a joint density function. (b) Find the marginal density of X . (c) Find the marginal density of Y . (d) Given Y = y find the conditional density of X . (e) P ( 1/2 < X < 1|Y =...