Let X and Y have the following joint distribution
X/Y | 0 | 1 |
0 | 0.4 | 0.1 |
1 | 0.1 | 0.1 |
2 | 0.1 | 0.2 |
a) Find Cov(4+2X, 3-2Y)
b) Let Z = 3X-2Y+2 Find E[Z] and σ 2Z
c) Calculate the correlation coefficient between X and Y. What does this suggest about the relationship between X and Y?
d) Show that for two nonzero constants a and b
Cov(X+a, Y+b) = Cov(X,Y)
Let X and Y have the following joint distribution X/Y 0 1 0 0.4 0.1 1...
(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...
Let X and Y have the following joint distribution: X/Y -1 1 0 0.2 0.15 2 0.1 0.2 4 0.25 0.1 a) Find the probability distributions for X and Y b) Find E[X] and E[Y] c) Find the probability that X is larger than 1 d) Find E[XY]
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. 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...
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Let (X,Y) have joint pdf given by f(x, y) = { Sey, 0 < x <y<, | 0, 0.W., (a) Find the correlation coefficient px,y (b) Are X and Y independent? Explain why.