If X is a RV with a continuous distribution function F(x), prove that Y = F(X) has(x- 1) 13x<3iff(x) =otherwisefind the range of Y corresponding to the range 1.1

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Answered: IfX is a RV with a continuous…

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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If F(x1, x2, x3) is the value of the joint distribution function of X1, X2, and X3 at (x1, x2, x3), show that the joint marginal distribution function of X1 and X3 is given by M(x1, x3) = F(x1, q, x3) for −q < x1 < q, −q < x3 < q and that the marginal distribution function of X1 is given by G(x1) = F(x1, q, q) for −q < x1 < q With reference to Example 19, use these results to find (a) the joint marginal distribution function of X1 and X3; (b) the marginal distribution function of X1.
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IfX is a RV with a continuous dištribution function F(x), prove that Y = F(X) has a uniform distribution in (0, 1). Further, (x-1) 1