Two random variables have the joint density funcitn as follows:
f(x,y)=x/y^2 , 0<x<y, 0<y<2
f(x,y)= 0, elsewhere
a) Find the marginal distribution of X
b)Find the marginal distribution of Y
c)Are X and Y statistically independent? (Justify your answer.)
d) Find f(x/y)
Two random variables have the joint density funcitn as follows: f(x,y)=x/y^2 , 0<x<y, 0<y<2 f(x,y)= 0,...
# 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?
5. If two random variables X and Y have the joint density k(52+2y2) for 0<<2 0 <y< 1 f(r, y) elsewhere (a) Find k (b) Find P(0<x< 1, 0<Y<0.5) (c) Find marginal density fi(a) and f2(y) (d) Are X and Y independent? (e) Find E(X) () Find P(X2 0.5). expression for fi(x|y); (g) an
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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
The joint probability density function for continuous random variables X and Y is given below. f (x) = x + y, 0 < x < 1, 0 < y < 1 if; 0, degilse. (a) Show that this is a joint density function. (b) Find the marginal density of X . (c) Find the marginal density of Y . (d) Given Y = y find the conditional density of X . (e) P ( 1/2 < X < 1|Y =...
The joint probability density function for continuous random variables X and Y is given below. f (x) = x + y, 0 < x < 1, 0 < y < 1 if; 0, degilse. (a) Show that this is a joint density function. (b) Find the marginal density of X . (c) Find the marginal density of Y . (d) Given Y = y find the conditional density of X . (e) P ( 1/2 < X < 1|Y =...
The joint probability density function for continuous random variables X and Y is given below. f (x) = x + y, 0 < x < 1, 0 < y < 1 if; 0, degilse. (a) Show that this is a joint density function. (b) Find the marginal density of X . (c) Find the marginal density of Y . (d) Given Y = y find the conditional density of X . (e) P ( 1/2 < X < 1|Y =...
Two random variables, X and Y, have joint probability density function f ( x , y ) = { c , x < y < x + 1 , 0 < x < 1 0 , o t h e r w i s e Find c value. What's the conditional p.d.f of Y given X = x, i.e., f Y ∣ X = x ( y ) ? Don't forget the support of Y. Find the conditional expectation E [...
The continuous random variables, X and Y , have the following joint probability density function: f(x,y) = 1/6(y2 + x3), −1 ≤ x ≤ 1, −2 ≤ y ≤ 1, and zero otherwise. (a) Find the marginal distributions of X and Y. (b) Find the marginal means and variances. (c) Find the correlation of X and Y. (d) Are the two variables independent? Justify.
The joint probability density function of the random variables X, Y, and Z is (e-(x+y+z) f(x, y, z) 0 < x, 0 < y, 0 <z elsewhere (a) (3 pts) Verify that the joint density function is a valid density function. (b) (3 pts) Find the joint marginal density function of X and Y alone (by integrating over 2). (C) (4 pts) Find the marginal density functions for X and Y. (d) (3 pts) What are P(1 < X <...