so, 2nd option is correct.
Suppose the difference between two variables is X-Y=Z, and its distribution isfx-Y (2) = fx (a)...
2. Suppose X and Y are independent continuous random variables. Show that P(Y < X) = | Fy(x) · fx (x) dx -oo where Fy is the CDF of Y and fx is the PDF of X [hint: P[Y E A] = S.P(Y E A|X = x) · fx(x) dx]. Rewrite the above equation as an expectation of a function of X, i.e. P(Y < X) = Ex[•]. Use the above relation to compute P[Y < X] if X~Exp (2)...
Suppose two continuous random variables X and Y have cumulative distribution functions Fx(x) and Fy(y) respectively. Suppose that Fx(x) > Fy(x) for all x. Indicate whether the following statements are TRUE or FALSE with brief explanation. (a) E(X) > E(Y) (b) The probability density functions fx, fy satisfy fx(x) > fy(x) for all x. (c) P (X = 1) > P (Y = 1)
Problem #5 (20 points) - Quotient of Two Random Variables Suppose that X and Y are independent positive continuous random variables with pdfs fx(x) and fy (y) and suppose that Z = X/Y. Show that the pdf of Z can be computed from the pdfs fx(x) and fy(y), using fz(2) = fx(yz)fy(y)ydy.
7.5.6 Random variables X and Y have joint PDF fx,y(x, y) = _J1/2 -1 < x <y <1, 1/2 10 otherwise. (a) What is fy(y)? (b) What is fx|v(x\y)? (c) What is E[X|Y = y)?
1. Let (X,Y) be a random vector with joint pdf fx,y(x,y) = 11–1/2,1/2)2 (x,y). Compute fx(x) and fy(y). Are X, Y independent? 2. Let B {(x,y) : x2 + y2 < 1} denote the unit disk centered at the origin in R2. Let (X',Y') be a random vector with joint pdf fx',y(x', y') = 1-'13(x',y'). Compute fx(x') and fy(y'). Are X', Y' independent?
There are two random variables X and Y. Let Z = X/Y. Determine the distribution of Z in terms of the joint distribution of X and Y using the pdf method.
1. Let X and Y be two jointly continuous random variables with joint CDF otherwsie a. Find the joint pdf fxy(x, y), marginal pdf (fx(x) and fy()) and cdf (Fx(x) and Fy)) b. Find the conditional pdf fxiy Cr ly c. Find the probability P(X < Y = y) d. Are X and Y independent?
For a random variable X with cumulative distribution function (cdf) Fx(x) = 1- (2/x)^2 ,x>2. (a).Find the pdf fX(x). (b).Consider the random variable Y = X^2. Find the pdf of Y, fY (y).
The joint density function of the continuous variables X and Y is fX,Y(x,y) = (12/5)*x*(2-x-y) for 0<X<1 and 0<Y<1. a) Find the expected value of X+Y. (b) Find fX(x), and fY(y). (c) Find Cov(X,Y). (d) Find Corr(X,Y).
1. Suppose that X and Y are random variables that can only take values in the intervals 0 X 2 and 0 Y 3 2. Suppose also that the joint cumulative distribution function (cdf) of X and Y, for 0 < 2 and 03 y 3 2, is as follows: Fy). 16 [5] (a) Determine the marginal cdf Fx(x) of X and the marginal cdf Fy () of Y [5] (b) Determine the joint probability density function (pdf) f(x, y)...