1) Area under PDF is always unity hence by using this property we can find k, therefore
3) Since the probability can't be negative the answer will be zero
The following joint probability distribution is given. 1. Find k such that the given function demonstrates...
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...
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...
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).
The joint probability density function (pdf) of (X,Y ) is given by f(X,Y )(x,y) = 12/ 7 x(x + y), for 0 ≤ y ≤ 1, 0 ≤ x ≤ 1, 0, elsewhere. (a) Find the cumulative distribution function of (X,Y ). Make sure you derive expressions for the cdf in the regions • x < 0 or y < 0; • 0 ≤ x ≤ 1, 0 ≤ y ≤ 1; • x > 1, 0 ≤ y ≤...
< 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).
4. The joint distribution of X and Y is given by 0 otherwise (a) Are X and Y independent? Explairn. (b) Find the marginal probability function (pdf) of Y, fy (). (c) Provide the integral for finding P(X < Y), but DO NOT evaluate.
[2.5 points] If two random variables have a joint density given by, f(x, y) = k(3x + 2y) 0 for 0 < x < 2, 0 < y < 1 elsewhere (a) Find k (b) Find the Marginal density of Y. (c) Find E(Y) (d) Find marginal density X. (e) Find the probability, P(X < 1.3). (f) Evaluate fı(x|y); (g) Evaluate fi(x|(0.75))
7. The random variables X and Y have joint probability density function f given by 1 for x > 0, |y| 0 otherwise. 1-x, Below you find a diagram highlighting the (r, y) pairs for which the pdf is 1 (a) Calculate the marginal probability density function fx of X (b) Calculate the marginal cumulative distribution function Fy of Y (c) Are X and Y independent? Explain.
7. The random variables X and Y have joint probability density function f given by 1 for x > 0, |y| 0 otherwise. 1-x, Below you find a diagram highlighting the (r, y) pairs for which the pdf is 1 (a) Calculate the marginal probability density function fx of X (b) Calculate the marginal cumulative distribution function Fy of Y (c) Are X and Y independent? Explain.
Given the joint probability density function f(x ,y )=k (xy+ 1) for 0<x <1--and--0<y<1 , find the correlation- r (X,Y) .