Problem 4 Determine the value of c that makes the function: fry(x,y)s cry for 0 <...
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.
4. Suppose two random variables X and Y has the following joint density function Cry, 22 Sy<1, f(x,y) = { 0, otherwise. (a) Find the constant C. (b) Find E(Y|X = 1/2). 5. Suppose X1, X2, ..., are i.i.d. random variables coming from the N(0,0%) population. (a) Determine the mean and variance for X. (b) Show that va bos (x2) – 1o60*) $ (0.2).
Suppose that X and Y are jointly continuous random variables with joint probability density function f(x,y) = {12rºy, 1 0, 0<x<a, 0<y<1 otherwise i) Determine the constant a ii) Find P(0<x<0.5, O Y<0.25) HE) Find the marginal PDFs fex) and y) iv) Find the expected value of X and Y. Le. E(X) and E(Y) v) Are X and Y independent? Justify your answer.
The joint probability density function of the random variables X, Y, and Z is (e-(x+y+z) f(x, y, z) 0 < x, 0 < y, 0 <z elsewhere (a) (3 pts) Verify that the joint density function is a valid density function. (b) (3 pts) Find the joint marginal density function of X and Y alone (by integrating over 2). (C) (4 pts) Find the marginal density functions for X and Y. (d) (3 pts) What are P(1 < X <...
1. Consider two random variables X and Y with joint density function f(x, y)-(12xy(1-y) 0<x<1,0<p<1 otherwise 0 Find the probability density function for UXY2. (Choose a suitable dummy transformation V) 2. Suppose X and Y are two continuous random variables with joint density 0<x<I, 0 < y < 1 otherwise (a) Find the joint density of U X2 and V XY. Be sure to determine and sketch the support of (U.V). (b) Find the marginal density of U. (c) Find...
Consider random variables X and Y with joint probability density function (Pura s (xy+1) if 0 < x < 2,0 <y S4, fx.x(x, y) = otherwise. These random variables X and Y are used in parts a and b of this problem. a. (8 points) Compute the marginal probability density function (PDF) fx of the random variable X. Make sure to fully specify this function. Explain.
The joint density function of continuous variables X and Y is (8 points) fry (x, y) = x y ; 0 < x < 1, 1 < y < 5 and= 0 elsewhere. i. Find the marginal density functions for X and Y, fx (x), fy (y). ii. Are X and Y independent?. Justify your answer.
Determine the value of c that makes the function f(x,y) = c(x+ y) a joint probability mass function over the nine points with x= 1, 2, 3 and y = 1, 2, 3. Determine the following: a) P(X = 1, Y < 4) b) P(X = 1) c) P(Y = 2) d) P(X < 2, Y < 2) e) E(X), E(Y), V(X), V(Y) f) Marginal probability distribution of the random variableX. g) Conditional probability distribution of Y given that X...
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...
Random variables X and Y share a joint probability density function: f(x,y) сух over the range 0< x <4 and 1 < y 5 otherwise Determine the following a. Value of c b. Marginal probability density function of X For the remaining parts of the problem, explain how you would determine the required information, including in your answer any necessary equations. Integration is not required for the remaining parts of this question; provided any required integrals are completely defined with...