If the joint density function of X and Y is given f(x,y) = {k(x + 2y), 0 < x < 1; 1

MATLAB: An Introduction with Applications
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If the joint density function of X and Y is given
f(x, y) = }KC*
(k(x+ 2y), 0 < x < 1; 1 < y < 2
0, elsewhere
a. Evaluate the value k.
b. Estimate P(X+Y < 2).
c. Find the marginal distribution of X and the marginal distribution of Y.
d. Calculate P (1<y<3/2/x=1/2).
e. Calculate P (0cxc1/2/y=3/2).
f. Find the expected value of X and the expected value of Y.
g. Determine whether the two random variables are dependent or independent.
h. Find the expected value of g(X, Y) = X/Y3 + X2Y.
i. Calculate the variance of X and the variance of Y.
j. Calculate the covariance of the random variables X and Y.
Transcribed Image Text:If the joint density function of X and Y is given f(x, y) = }KC* (k(x+ 2y), 0 < x < 1; 1 < y < 2 0, elsewhere a. Evaluate the value k. b. Estimate P(X+Y < 2). c. Find the marginal distribution of X and the marginal distribution of Y. d. Calculate P (1<y<3/2/x=1/2). e. Calculate P (0cxc1/2/y=3/2). f. Find the expected value of X and the expected value of Y. g. Determine whether the two random variables are dependent or independent. h. Find the expected value of g(X, Y) = X/Y3 + X2Y. i. Calculate the variance of X and the variance of Y. j. Calculate the covariance of the random variables X and Y.
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