. Let X and Y be the proportion of two random variables with joint probability density...
. Let X and Y be the proportion of two random variables with joint probability density function f(r, y) e-*, 0, if, 0 < y < x < oo, elsewhere. a) Find P(Xc3.y-2). b) Are X and Y independent? Why? c) Find E(Y/X)
. Let X and Y be the proportion of two random variables with joint probability density function f(x, y)o, elsewhere. (a) Find P(X < 3|Y= 2). (b) Are X and Y independent? Why? (c) Find E(Y/X)
Let X and Y be two continuous random variables having the joint probability density 24xy, for 0 < x < 1,0<p<1.0<x+y<1 0, elsewhere Find the joint probability density of Z X + Y and W-2Y.
1. a) Let X and Y be random variables with the following joint probability density function (pdf) Зу f(x,y) = 0<y< 2x2,0<x< 1. 2.02 i) Obtain the value for E(Y|X = }). ii) Show the relationship between E[Y|X] and E[XY]. Use this result to obtain E[XY]
4.5-5 Two random variables X and Y have a joint probability density function ability, 0<y<x<2 om oldalon ( 52 fxy(x, y) = 16 o Wes and m Signal es elsewhere to (a) Find the marginal density functions of X and Y. (b) Are X and Y statistically independent? oldoro ototitillarindanand
1. Let X and Y be random variables with joint probability density function flora)-S 1 (2 - xy) for 0 < x < 1, and 0 <y <1 elsewhere Find the conditional probability P(x > ]\Y < ).
Let the joint density function of random variables X and Y be f(x,y) = 8 - x - y) for 0 < x < 2, 2 < y < 4 0 elsewhere Find : (1) P(X + Y <3) (11) P(Y<3 | X>1) (111) Var(Y | x = 1)
If two random variables have the joint density (x + y2), for 0 < x < 1, 0 < y < 1 0, elsewhere. find the probability that 0.2 < X < 0.5 and 0.4 <Y < 1.6. With reference to the previous Problem 6, find both marginal densities and use them to find the probabilities that a. X > 0.8; b. Y < 1.5.
# 6 If two random variables have the joint density f(x, y)=59 y?) for 0<x<1, 0<y<1 0 elsewhere a. Find the probability that 0.2 X<0.5 and 0.4<Y<0.6. b. Find the probability distribution function F(x, y). c. Are x and y independent?
[2.5 points] If two random variables have a joint density given by, f(x, y) = k(3x + 2y) 0 for 0 < x < 2, 0 < y < 1 elsewhere (a) Find k (b) Find the Marginal density of Y. (c) Find E(Y) (d) Find marginal density X. (e) Find the probability, P(X < 1.3). (f) Evaluate fı(x|y); (g) Evaluate fi(x|(0.75))