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the joint probability density
function is given by
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).
1. Determine the constant c such that the given function is a valid joint PDF for the jointly continuous random variables X and Y. f(x,y) ={cry otherwise 0 < y < 2x a. Find the value of the constant c. b. Find the marginal PDFs for X and Y. Are X and Y independent?
Let X1 and X2 have a joint pdf
Let
Find the joint pdf of Y1 and Y2.
f(x, y) = + y, 0<x,y<1
< 1. The joint probability density function (pdf) of X and Y is given by for(x, y) = 4 (1 - x)e”, 0 < x <1, 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).
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...
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...
for example,given joint pdf of function is 2x but intervals are 0<x<y<2. (it may be invalid pdf) When i find marginal pdf of y,i will take interval of (0,y) and integrate it with respect to x,(x,2) and integrate it with respect to y. Do i need to use interval of 0<x<2 in any circumstance?
The joint probability density function (PDF) of random variables X and Y is given by: f(x,y) = 4xy for 0 ≤ y ≤ x ≤ 1, and = 0 elsewhere The mean of the random variable X is:
If the joint pdf of (X,Y) is given by f(x,y) =3xy(x+y) , 0≤x , y≤1 ; find the value of E{E(Y/X)} , E(Y).
How to get the cdf when y>x>0? Thanks
6. The joint probability density function (pdf) of (X, Y) is given by 0y<oo, elsewhere. fxr, y) (a) Find the cumulative distribution function of (X, Y) (b) Evaluate P(Y < X2) (c) Derive the pdf of X and then compute the mean and variance of X (d) Find the pdf of Y and compute the mean and variance of Y (e) Calculate the conditional pdf of Y given X (f) Compute the...