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7. Let RVs Yand Yhave the following joint pdf f(x,y)=L if 1 srs2,1Sys2 0, otherwise a)...
Let X and Y be continuous rvs with a joint pdf of the form: ?k(x+y), if(x,y)∈?0≤y≤x≤1? f(x,y) = 0, otherwise (a) Find k. (b) Find the joint CDF F (x, y). 0, otherwise (c) Find the conditional pdfs f(x|y) and f(y|x) (d) Find P[2Y > X] (e) Find P[Y + 2X > 1]
Consider two rvs Xand Ywith joint pdf f(x,y)-k-y, 0<y<x 1 Find the value of the pdf of U=X+ Y evaluated at u = 0.8. Hence, or otherwise, estimate P(0.8<XY<0.801) Consider two rvs Xand Ywith joint pdf f(x,y)-k-y, 0
2. A continuous random variable has joint pdf f(x, y): xy 0 x 1, 0sys 2 f(x, y) otherwise 0 a) Find c b) Find P(X Y 1) b) Find fx(x) and fy(v) c) Are X and Y independent? Justify your answer d) Find Cov(X, Y) and Corr(X, Y) e) Find fxiy (xly) and fyixylx)
4. Two RVs with a joint pdf given as follows fx.x ), 0<x< 1,0 <y<1 otherwise (a) Find fr ). (6 point) (b) Find fxy(x[y). (6 points) (c) Are X and Y independent? (clearly show justification for credit) (6 points)
Suppose X and Y have the joint pdf f (x, y) = 3y, 0 < y < 1, y − 1 < x < 1 − y 0 otherwise a) Give an expression for P (X > Y ). b) Find the marginal pdfs for Y . c) Find the conditional pdf of X given Y = y, where 0 < y < 1. d) Give an expression for E[XY ]. e) Are X and Y independent?
Problem 3: (15 points) The random variables X and Y have the joint PDF otherwise 1) Determine the marginal PDFs fx(x) and fy (y) 2 Determine EX and E[Y: 3) Determine Cov[X, Y]
0 〈 y 〈 x2く1· Consider two rvs X and Y with joint pdf f(x,y) = k-y, (a) Sketch the region in two dimensions where fx,y) is positive. Then find the constant k and sketch ) in three imesions Then find the constant k and sketch f(r.y) in three dimensions (b) Find and sketch the marginal pdf fx), the conditional pdf(x1/2) and the conditional cdf FO11/2). Find P(X〈Y! Y〉 1/2), E(XİY=1/2) and E(XIY〉l/2). (c) What is the correlation between X...
please show steps Q.8 Let X and Y be continuous rvs with the joint pdf f(x, y) = (3/2)xy, for 0 < x, 0 < y, 0 < x + y < 2 and 0 otherwise. (a) Find E[X + Y ] and E[X − Y ] (b) Find E[XY ] (c) Find E[Y |X = x] and E[X|Y = y]. (d) Find Cov[X, 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?
4. (Sec. 5.2, 00) Let X and Y be continuous rvs with the joint f(x, y) = 2(x+y), for 0 <y <r <1 and 0 otherwise. (a) Find E(X+Y) and E[X - Y) (b) Find E[XY] (c) Find E[Y|X = x) and E[X Y = y). (d) Find Cov[X,Y]