Let the joint pdf of X and Y be ,
zero elsewhere. Let U = min(X, Y ) and V = max(X, Y ). Find the joint pdf of U and V .
Let the joint pdf of X and Y be , zero elsewhere. Let U = min(X, Y ) and V = max(X, Y ). Find the joint pdf of U and V...
1. Let (X, Y) X, Y be two random variables having joint pdf f xy (xy) = 2x ,0 «x « 1,0 « y« 1 = 0, elsewhere. Find the pdf of Z = Xy?
3). Let X and Y be two random variables with the joint pdf 41-, 0<b< 0<pく1; 6x f (,)0 elsewhere. ǐf 0 < z < 1; Find Pr(X >1/v=1). 3). Let X and Y be two random variables with the joint pdf 41-, 0
Let X and Y denote independent random variables with respective probability density functions, f(x) = 2x, 0<x<1 (zero otherwise), and g(y) = 3y2, 0<y<1 (zero otherwise). Let U = min(X,Y), and V = max(X,Y). Find the joint pdf of U and V.
Q3: Let X and Y have the joint pdf f(x,y)- c(x-y) 0sysrs1, and 0 elsewhere. a) Find c b) Find P(x > hY) c) Find P(X S 2Y) d) Find the marginal pdf for X and Y
1) Let X and Y have joint pdf: fxy(x,y) = kx(1 – x)y for 0 < x < 1,0 < y< 1 a) Find k. b) Find the joint cdf of X and Y. c) Find the marginal pdf of X and Y. d) Find P(Y < VX) and P(X<Y). e) Find the correlation E(XY) and the covariance COV(X,Y) of X and Y. f) Determine whether X and Y are independent, orthogonal or uncorrelated.
Step by step solution 1. Let X and Y be two random variable with joint pdf f(x, y) 3r for 0 SySIS 1, and zero elsewhere. (a) Compute P(O<X 05nY 2 0.25) (b) Compute marginal densities of X and Y
Suppose that: (a) Let V = XY . Find the joint pdf for (X, V ). Use it to get the pdf for V . (b) What is the conditional pdf for X, given V = v? What does this say about the relationship between X and V ? (c) Show that Z = X + Y has pdf (Do not try to simplify it.)
(7) Let X1,Xn are i.i.d. random variables, each with probability distribution F and prob- ability density function f. Define U=max{Xi , . . . , X,.), V=min(X1, ,X,). (a) Find the distribution function and the density function of U and of V (b) Show that the joint density function of U and V is fe,y(u, u)= n(n-1)/(u)/(v)[F(v)-F(u)]n-1, ifu < u. (7) Let X1,Xn are i.i.d. random variables, each with probability distribution F and prob- ability density function f. Define U=max{Xi...
Let X and Y be a random variable with joint PDF: f X Y ( x , y ) = { a y x 2 , x ≥ 1 , 0 ≤ y ≤ 1 0 otherwise What is a? What is the conditional PDF of given ? What is the conditional expectation of given ? What is the expected value of ? Let X and Y be a random variable with joint PDF: fxv (, y) = {&, «...
Let X and Y have joint pdf f(x, y)= e if 0 < x < y< o and zero otherwise. Find Е(X |у). 16.