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there is no need to introduce new variables 2. Consider a joint pdf Find: (a) E(X|Y = y). (b) E(Y|X =x). (c) E(XY) 2. Consider a joint pdf Find: (a) E(X|Y = y). (b) E(Y|X =x). (c) E(XY)
2. Let the random variables X and Y have the joint PDF given below: (a) Find P(X + Y ≤ 2). (b) Find the marginal PDFs of X and Y. (c) Find the conditional PDF of Y |X = x. (d) Find P(Y < 3|X = 1). Let the random variables X and Y have the joint PDF given below: 2e -0 < y < 00 xY(,) otherwise 0 (a) Find P(XY < 2) (b) Find the marginal PDFs of...
1. Suppose X and Y are continuous random variables with joint pdf f(x,y) 4(z-xy) if = 0 < x < 1 and 0 < y < 1, and zero otherwise. (a) Find E(XY) b) Find E(X-Y) (c) Find Var(X - Y) (d) What is E(Y)?
Consider the following joint PDF of continuous random variables X and Y: 22 – 2pxy + y2 2(1 - 02) where pe(-1,1). (a) Prove that fx,y(x, y) is a joint PDF function. (b) What is the marginal PDF of X? (c) Calculate E[XY] – E[X]E[Y]. (d) Prove that X and Y are independent if and only if p= 0 (e) Show that the conditional PDF of X, given Y = y is N(py, 1 – p2.
Let X and Y be continuous random variables with joint pdf f(x,y) =fX (c(X + Y), 0 < y < x <1 otBerwise a. Find c. b. Find the joint pdf of S = Y and T = XY. c. Find the marginal pdf of T. 、
1. Let (X, Y) X, Y be two random variables having joint pdf f xy (xy) = 2x ,0 «x « 1,0 « y« 1 = 0, elsewhere. Find the pdf of Z = Xy?
2. Let the joint pdf of X and Y be given by f(xy)-cx if 0sysxsi Determine that value of c that makes f into a valid pdf. a. Find Pr(r ) b 2 C. Find Prl X d. Find the marginal pdf's of X and Y e. Find the conditional pdfs of 자리 and ri- f. Are X and Y independent? Give a reason for your answer g. Find E(X), E(Y), and E(X.Y) 2. Let the joint pdf of X...
3. Consider two random variables X and Y with the joint probability density (a)o elsewhere which is the sane asin Question I. Now let Z = XY 2 and U = X be a joint transformation of (X, Y). (a) Find the support of (Z, U) (b) Find the inverse transformation (c) Find the Jacobian of the inverse transformation. (d) Find the joint pdf of (Z, U) (e) Find the pdf of Z XY from the joint pdf of (Z,...
2. Consider random variables X and Y with the following joint PDP: 2xyn (a) Suppose that U-In(XY) and V- In(X). Express X and Y in terms of U and V. (b) Use part (a) to find the Jacobian of the transformation from (X, Y) 'to (U, v) (c) Use (a) and (b) to show that the joint PDF of U and V is:
5. Suppose that the joint pdf of the random variables X and Y is given by - { ° 0 1, 0< y < 1 f (x, y) 0 elsewhere a) Find the marginal pdf of X Include the support b) Are X and Y independent? Explain c) Find P(XY < 1)
Problem 4 Suppose X and Y have joint PDF Ixr(zy)-{0,y, otherwise, o< <p (a) Find E[XY] (b) Find E[X] (c) Find the Covariance of X and Y