For questions 5-8, consider the following experiment: Suppose the location of a particle in the p...
55. Let X and Y be jointly continuous random variables with joint density function fx.y(x,y) be-3y -a < x < 2a, 0) < y < 00, otherwise. Assume that E[XY] = 1/6. (a) Find a and b such that fx,y is a valid joint pdf. You may want to use the fact that du = 1. u 6. и е (b) Find the conditional pdf of X given Y = y where 0 <y < . (c) Find Cov(X,Y). (d)...
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.
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...
1. Let X and Y be two jointly continuous random variables with joint CDF otherwsie a. Find the joint pdf fxy(x, y), marginal pdf (fx(x) and fy()) and cdf (Fx(x) and Fy)) b. Find the conditional pdf fxiy Cr ly c. Find the probability P(X < Y = y) d. Are X and Y independent?
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)?
MA2500/18 Section B (Answer THREE questions) 6. Let X and Y be jointly continuous random variables defined on the same prob- ability space, let fx.y denote their joint PDF, and let fx and fy respectively denote their marginal PDFs (a) Let z be a fixed value such that fx(x) >0. Write down expressions for 12] (i) the conditional PDF of Y given X = z, and (i) the conditional expectation of Y given X (b) State and prove the law...
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...
Suppose that X and Z are zero-mean jointly normal random variables, such that of = 4,02 = 17/9, and E [XZ] = 2. We define a new random variable Y = 2X – 3Z. Determine the PDF of Y, the conditional PDF of X given Y, and the joint PDF of X and Y.
Let X, Y be jointly continuous with joint density function (pdf) fx,y(x, y) *(1+xy) 05 x <1,0 <2 0 otherwise (a) Find the marginal density functions (pdf) fx and fy. (b) Are X and Y independent? Why or why not?
Problem 3: X and Y are jointly continuous with joint pdf 0<x<2, 0<y<x+1 f(x,y) = 17 0, Elsewhere a) Find P(X < 1, Y < 2). b) Find marginal pdf's of X. c) f(x|y=1). d) Find E(XY). dulrahim