# 11 11. If X U(0.1) and Y (0,1) independent random variables, find the joint pdf...
2. Let X and Y be independent, standard normal random variables. Find the joint pdf of U = 2X +Y and V = X-Y. Determine if U and V are independent. Justify.
Let X and Y be independent exponential random variables with parameter 1. Find the joint PDF of U and V. U = X + Y and V = X/(X + Y)
Suppose the joint pdf of random variables X and Y is f(x,y) = c/x, 0 < y < x < 1. a) Find constant c that makes f (x, y) a valid joint pdf. b) Find the marginal pdf of X and the marginal pdf of Y. Remember to provide the supports c) Are X and Y independent? Justify
5. If X and Y are independent and identically distributed with Exponential(A), compute El and 6. Let R be the region bounded by the points (0, 1), (-1,0) and (1,0). Joint pdf of (x, Y) is: 1, if (r,y) e R 0, otherwise. Compute P(X-1, γ 7. If X U(0,1) and Y U(0, 1) independent random variables, find the joint pdf of (X+y,x -Y). Also compute marginal pdf of X+Y 8. If x Ezpomential(0.5) and Y ~ Erponential0.5) independent random...
Problem 5 Let X and Y be random variables with joint PDF Px.y. Let ZX2Y2 and tan-1 (Y/X). Θ i. Find the joint PDF of Z and Θ in terms of the joint PDF of X and Y ii. Find the joint PDF of Z and Θ if X and Y are independent standard normal random variables. What kind of random variables are Z and Θ? Are they independent? Problem 5 Let X and Y be random variables with joint...
1. Consider a pair of random variables (X, Y) with joint PDF fx,y(x, y) 0, otherwise. (a) 1 pt - Find the marginal PDF of X and the marginal PDF of Y. (b) 0.5 pt - Are X and Y independent? Why? (e) 0.5 pt - Compute the mean of X and the mean of Y.
5. Suppose that the joint pdf of the random variables X and Y is given by - { ° 0 1, 0< y < 1 f (x, y) 0 elsewhere a) Find the marginal pdf of X Include the support b) Are X and Y independent? Explain c) Find P(XY < 1)
The joint PDF of random variables X and Y is expressed as (a) Determine the constant c. (b) Determine the marginal density function for X. (c) Determine the marginal density function for Y. (d) Are X and Y statistically independent? (e) Determine the probability of P(X ≤ 0.5 | Y = 1). The joint PDF of random variables X and Y is expressed as certy, 05xs1 and 05ys2 fx.x(x, y) = 10. elsewhere. (a) Determine the constant c. (b) Determine...
4. Let X and Y be random variables of the continuous type having the joint pdf f(x,y) = 1, 0<x< /2,0 <y sin . (a) Draw a graph that illustrates the domain of this pdf. (b) Find the marginal pdf of X. (c) Find the marginal pdf of Y. (d) Compute plx. (e) Compute My. (f) Compute oz. (g) Compute oz. (h) Compute Cov(X,Y). (i) Compute p. 6) Determine the equation of the least squares regression line and draw it...
7. Suppose the random variables (X, Y) have joint pdf given by Ta ſ cx2y2 if 0 <x sys1, l o otherwise. a. Find the constant c. b. Find the marginal density of X. c. Find the marginal density of Y. d. Are X and Y independent?