* The joint pdf of x and Y is Fxy (x,y) = cx^3 y , 0 <x<y<1 .
A) find the value of C to make this a valid pdf?
* The proportion of defective parts shipped by a wholesaler varies from shipment to shipment. Suppose that the proportion of defective in shipment follow a beta distribution with a=4 and B = 2 .
A) what is the probability that a shipment will have fewer than 20% defective parts ?
The joint pdf of X and Y is fxy(x,y) = cx^3y, 0 < x < y < 1 a.) Find the value of c to make this a valid pdf. b.) Are x and y independent?
2. Suppose X and Y have the joint pdf fxy(x, y) = e-(x+y), 0 < x < 00, 0 < y < 0o, zero elsewhere. (a) Find the pdf of Z = X+Y. (b) Find the moment generating function of Z.
Let the random variables X, Y with joint probability density function (pdf) fxy(z, y) = cry, where 0 < y < z < 2. (a) Find the value of c that makes fx.y (a, y) a valid pdf. (b) Calculate the marginal density functions for X and Y (c) Find the conditional density function of Y X (d) Calculate E(X) and EYIX) (e Show whether X. Y are independent or not.
1. The joint probability density function (pdf) of X and Y is given by fxy(x, y) = A (1 – xey, 0<x<1,0 < y < 0 (a) Find the constant A. (b) Find the marginal pdfs of X and Y. (c) Find E(X) and E(Y). (d) Find E(XY). 2. Let X denote the number of times (1, 2, or 3 times) a certain machine malfunctions on any given day. Let Y denote the number of times (1, 2, or 3...
Q3. Suppose that X, Y have joint pdf a for x2 + y2 0 otherwise. 1. fxy(x, y)- (a) Find the value of a so that fxy(x, y) is a valid pdf. b) Find the marginal pdf for X Hint: It is helpful to sketch the region of the ry-plane where the pdf is non-zero
Suppose X, Y are random variables whose joint PDF is given by fxy(x,y) = { 0<y<1,0<=<y 0, otherwise 1. Find the covariance of X and Y. 2. Compute Var(X) and Var(Y). 3. Calculate p(X,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.
Suppose X, Y are random variables whose joint PDF is given by fxy(x, y) 9 { 0 <y <1,0 < x <y y otherwise 0, 1. Find the covariance of X and Y. 2. Compute Var(X) and Var(Y). 3. Calculate p(X,Y).
The joint pdf of random variables X and Y is fxy(x, y) = ce-re-y , The pdf is zero everywhere else. a) Find the value of c. You need to do the calculation and get a value of c. bies A snd independenrt a Find the conditional ps /sy ad Define the ranges over which the conditional pdfs are defined The joint pdf of random variables X and Y is fxy(x, y) = ce-re-y , The pdf is zero everywhere...
5. The joint PDF of X and Y is given by s 3 fxy(x, y) = 3 o 0<x<3, 1<y<2, otherwise. Determine P[X<Y]. (8 pts)