1) Let X be exponential distributed with parameter d. Determinethe probability density function of yX-3X + 12) Let A CR² be the triangle given by (0,0), (1,0), (0, 1). Let(x, y) be uniformly distributed in A.a) determine the propability density function of (x, y)b) SHow that x and yare dependentc) the cumulative distribution function of X for OEX EIis given by fx (x)=2x-x²1) show by using probability density function11) show by using direct area determination

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Answered: • Let X be exponential distributed with…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose that the random variables X and Y have a joint density function given by: f(x,y)={cxy for 0≤x≤2 and 0≤y≤x, 0 otherwise Find the constant c, P(Y≥1/2), P(X < 2, Y >1/2), P(X < 1), Determine whether X and Y are independent.
Suppose that the random variables X and Y have a joint density function f(x,y).prove that Cov(X,Y)=0 if E(X|Y=y) does not depend on y
Suppose that the random variables X and Y have a joint density function given by: f(x,y)={cxy for 0≤x≤2 and 0≤y≤x, 0 otherwise c=1/2 P(X < 1), Determine whether X and Y are independent
Let X be a continuous random variable with density function f(x) = 2x, 0 ≤ x ≤ 1. Find the moment-generating function of X, M(t), and verify that E(X) = M′(0) and that E(X2) = M′′(0).
Suppose that X, Y are jointly continuous with joint probability density function f( x, y){ xe^-x(1+y), ifx >0 and y >00, otherwise. (a) Find the marginal density functions of X and Y. (b) Calculate the expectation E[XY]. (c) Calculate the expectation EIX/(1+ Y )1. (e) Determine if the random variables X and Y in this exercise are independent.
If X and Y are independent exponential random variables, each having parameter λ.(a) Find the joint density function of U = X + Y by using the convolution of fX and fY .(b) Find the joint density function of V = X − Y by using the method of transformation.(c) Are U and V independent?
The random vector (X, Y ) has the following joint probability density function:f(X,Y )(x, y) = 4xye^−(x2+y2), x > 0, y > 0,0 , otherwiseLet Z =√(X^2 + Y ^2) . Find the probability density of the random variable Z.
Suppose that X and Y have a joint probability density function f(x,y)= 1, if0<y<1,y<x<2y; 0, otherwise. (a) Compute P(X + Y less than or equal 1). (b) Find the marginal probability density functions for X and Y , respectively. (c) Are X and Y independent?
Let X be a continuous random variable with density function f(x) = {2x if x ∈ [0,1] {0 otherwise Compute E[X] and E(X2).
Let X, Y be random variables, suppose X is N(0, 1) and Y = e2X. a) Obtain the density function of Y .b) Calculate E(Y) and V ar(Y).
Let X and Y be two independent random variables with densities fX(x) = e^(-x), for x>0 and fY(y) = e^y, for y<0, respectively. Determine the density of X+Y.
5.)Suppose X is continuously uniformly distributed on [1, 4]. Let Y = ln(X). What is the density function for Y ? (Include the bounds for Y .)

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• Let X be exponential distributed with parameter 1. Determi the probability density function of y = X-3 X + 1