7. Let X and Y be continuous random variables with joint probability densityfunction given byfxy(xy):Sc,(0,0 < x < y < 1otherwisea) Find the value of c.b) Find the marginal distributions of X and Y.c) Find the conditional distribution of Y given X.d) Find the E(Y) and Var(Y).

Let and be continuous random variables with joint probability density function is given byWhere,…

Answered: . Let X and Y be continuous random…

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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5. Suppose that two continuous random variables X and Y have joint probability density function (e**y +e 2x-y) 15xs2,0sys3 elsewhere a. P( 3/2 s Xs2, 1SYS2) b. Are the random variables X and Y independent? c. find the conditional density X given Y = 0 d. Find the strength of the relationship and interpret the findings.
1)Let x and y be two continuous random variables whose function is the probability density joint is given by : a)Draw the relationship between the variables x and y on the Cartesian axes .b)Calculate the marginal pdfs px(X)and py(Y).c)Are the v.a.s x and y independent ?
1) Let x be a uniform random variable in the interval (0, 1). Calculate the density function of probability of the random variable y where y = − ln x.
Let X1, X2, . X6 be an i.i.d. random sample where each X, is a continuous random variable with probability density function f(x) = e-(-0) , x > 0 Find the probability density function for X(6).
The joint density function of two continuous random variables X and Y is fxy(x, y) = (2x+y) if 2
11. Let X be a continuous random variable with probability density function r>0 f(x)= 0, otherwise, where 1> 0. Let Y be the largest integer less than or equal to X. Determine the probability function of Y.
7. Let X and Y denote two continuous random variables. Let f(x,y) denote the joint probability density function and fx(x) and fy (y) the marginal probability density functions for X and Y, respectively. Finally let Z = aX + bY, where a and b are non-zero real numbers. (e) Derive an expression for Cov(Z) as a function of Var (X), Var(Y) and Cov(X,Y). [You may use standard results relating to variance and covariance without proof, but these should be clearly stated.]
1. A continuous random variable X is defined by (3+x) f(x) - 3sxs-1 %3D 16 (6-2r) -1sxs1 16 (3-x) -1sxs3 16 a. Verify that f(x) is density. Explain b. Find the mean 2. If the probability density function of random variable is given by f(x) = wch 1srs2 sech x a. Find the mean b. Find the total area 3. If the probability density function of random variable is given by f(x) = sinh 2x 1sxs2 a. Find the mean b. Find the total area c. Illustrate the graph (use bell shaped figure) II II
Let X and Y random variables have independent Gamma distributions with X-Gamma(1, 6) and Y-Gamma(2, B). a. Find the joint probability density of Z, = X + Y, Z, = X+Y a. Find the marginal pdf of Z2.
b) Let Y1, Y2.,Y5 be independent random variables with probability density function y 1 e 4 4 f(y)= ,y > 0 ,elsewhere 3 Determine the distribution and parameter of V = EY; using the method of moment i=1 generating function. Hence, find the mean of V using the moment generating function.
Suppose that X and Y are independent and uniformly distributed random variables. Range for X is (−1, 1) and for Y is (0, 1). Define a new random variable U = XY, then find the probability density function of this new random variable.
3. Let X and Y be two independent random variables with identical probability density function given by e- for x > 0 f(x) = elsewhere. What is the probability density function of W= max{X, Y } ?

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. Let X and Y be continuous random variables with joint probability density function given by Sc, fxy(xy) = {C 10, 0 < x < y < 1 otherwise a) Find the value of c. b) Find the marginal distributions of X and Y. c) Find the conditional distribution of Y given X. d) Find the E(Y) and Var(Y).