If the joint density function of X and Y is
f(x,y)=c(x^2−y^2)e^(−2x),
with 0≤x<∞and −x≤y≤x find each of the following.
(a) The conditional probability density of X,
given Y=y>0.
Conditional density fX|Y(x,y)=
(Enter your answer as a function of x, with y as a
parameter.)
b. Find the marginal density of the critical thinking test score, and evaluate it at the point Y=1/3
If the joint density function of X and Y is f(x,y)=c(x^2−y^2)e^(−2x), with 0≤x<∞and −x≤y≤x fin...
(1 point) If the joint density function of X and Y is f(x, y) = c(22 - y2)e- with OS: < oo and I y I, find each of the following. (a) The conditional probability density of X given Y = y >0. Conditional density fxy(:, y) = (Enter your answer as a function of I, with y as a parameter.) (b) The conditional probability distribution of Y given X = 2. Conditional distribution Fyx (2) = (Enter your answer...
I only need an answer for the second question because I know 9/16 is incorrect. (1 point) Applicants for jobs at a call centre take two tests, one for communication skills and the other on IT skills, and normalized scores are recorded on each between 0 and 2. For a given applicant, let X be the score on the communications test and Y the score on the IT test. A model for the joint probability density function for the two...
Consider fx (x)=e*, 0<x and joint probability density function fx (x, y) = e) for 0<x<y. Determine the following: (a) Conditional probability distribution of Y given X =1. (b) ECY X = 1) = (c) P(Y <2 X = 1) = (d) Conditional probability distribution of X given Y = 4.
A joint probability density function is given by f(x,y)-c-x(2-x-y), for 0 < x < 1 and 0 < y < 1. Find the value of c to make this a valid density function. A joint probability density function is given by f(x,y)-c-x(2-x-y), for 0
The joint probability density function of random variables X and Y is given by f(x,y) ={10xy^2 0≤x≤y≤1,0 otherwise. (a) Compute the conditional probability fX|Y(x|y). (b) Compute E(Y) and P(Y >1/2). (c) Let W=X/Y. Compute the density function of W. (d) Are X and Y independent? Justify briefly.
1. Consider the joint probability density function 0<x<y, 0<y<1, fx.x(x, y) = 0, otherwise. (a) Find the marginal probability density function of Y and identify its distribution. (5 marks (b) Find the conditional probability density function of X given Y=y and hence find the mean and variance of X conditional on Y=y. [7 marks] (c) Use iterated expectation to find the expected value of X [5 marks (d) Use E(XY) and var(XY) from (b) above to find the variance of...
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 [...