3. Consider the joint probability distribution for Y and X. X/Y 2 4 6 1 0.2...
(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...
. Suppose we have the following joint distribution for random variables X and Y 2 0.1 0.2 0.1 4 0 0.3 0.1 6 0 0 0.2 (a) Find p(X). That is find the marginal distribution of X. (b) Find p(Y). That is find the marginal distribution of Y (c) Find the distribution of X conditional on Y = 3. (d) Find the distribution of X conditional on Y 2 (e) Are X and Y independent? You should be able to...
Please provide correct answer (Very Important) Consider the following joint probability distribution: y fxY (x, y) -1.0 -3 1/8 -0.4 -1 1/4 0. 4 1 1/16 1. 0 3 9/16 Determine the following: (a) Conditional probability distribution of Y given that X = 1 fyll(y) = for y = (b) Conditional probability distribution of X given that Y = 1 fxli (x) = for x = (c) E(X|Y = 1) = (d) Are X and Y independent?
Suppose the joint probability distribution of two binary random variables X and Y are given as follows. x/y 1 2 0 3/10 0 1 4/10 3/10 X goes along side as 0 and 1, Y goes along top as 1 and 2. a) Show the marginal distribution of X. b) Find entropy H(Y ). c) Find conditional entropy H(X|Y ) and H(Y |X). d) Find mutual information I(X; Y ). e) Find joint entropy H(X, Y ). f) Suppose X...
Determine the value of c that makes the function f(x,y) = c(x+ y) a joint probability mass function over the nine points with x= 1, 2, 3 and y = 1, 2, 3. Determine the following: a) P(X = 1, Y < 4) b) P(X = 1) c) P(Y = 2) d) P(X < 2, Y < 2) e) E(X), E(Y), V(X), V(Y) f) Marginal probability distribution of the random variableX. g) Conditional probability distribution of Y given that X...
Q(2) The joint probability distribution of X and Y is given by (2x-y)2 for x = 0, 1, 2 and y = 1,2,3 (Marks: 6,2,4) 30 f(x, y) = Find : (1) the joint probability distribution of U = 3X + Y and V = X - 2Y (11) the marginal distribution of U. (III) E (V)
3. Let X and Y have a discrete joint distribution with Table 1: Joint discrete distribution of X and Y Values of Y -1 0 1 Values of X -1 1 į 0 1 1 0 -600-100 Then, find the following: • the marginal distribution of X; [2 points) • the marginal distribution of Y; [2 points] the conditional distribution of X given Y = -1; [2 points] Are X and Y are independent? Discuss with proper justification. (3 points)...
1. Consider the joint distribution fXY (x, y) = k · x y (1) over the domain 0 < x < 1, 0 < y < 1, for some k > 0. (a) What value should k have for f to be a proper density? (b) Find the marginal densities of X and Y . Hint: x y = exp[y · log(x)]. (c) Find the mean of Y . (d) Find the conditional mean of Y , given X
Suppose the joint probability distribution of two binary random variables X and Y are given as follows. X/Y 1 0 1 2 1 4 0 + 1 (a) Show the marginal distribution of X. [2pts] (b) Find entropy H(Y). [2pts] (e) Find conditional entropy H(XY). (3pts] (d) Find mutual information I(X;Y). [3pts] 2 (e) Find joint entropy H(X,Y). (3pts) Note: The following three proofs are not related to the example in parts (a - e). You need to prove each...