B3. Let us consider two discrete uniform distributions X - U({1,2,..., k}) and Y -U({0, k}). Compute the probability generating functions (p.g.f.s) of X and Y. If Xand Y are assumed to be independent, use these p.g.f.s to obtain the p.g.f. of X + Y.What is then the distribution of X +Y?Hint: You may want to use "1-zP+11-rfor x + 1, and that (a+b)(a-b) = a² - bn=0

Answered: Image /qna-images/answer/608da25c-6bd2-44e8-bad8-36e91f184c3f.jpg

Answered: 3. Let us consider two discrete uniform…

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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statistic discrete rondom variable
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1Example 23. A distribution x1, X2,..., Xp., Xp with frequencies, fp f2,..., f..., fn is transformed into the distribution y1, y2,.….., Y,.., yn with the same corresponding frequencies by the relation y, = ax, + b, where a and b are constants. Show that the mean, median and mode of the new distribution are given in terms of the first distribution by the same transformation.
D5) X and Y are two points that are selected according to a uniform distribution. Calculate the expected value of the distance between these two points for each of the following cases: a) Both X and Y are selected independently from the range 0-1. b) We select X between 0 and 1 and then select Y between 0 and X. Note: For case b the distance is equal to |Y-X|
If f (x) = cx and 0

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3. Let us consider two discrete uniform distributions X ~ U({1,2,..., k}) and Y U({0, k}). Compute the probability generating functions (p.g.f.s) of X and Y. If X and Y are assumed to be independent, use these p.g.f.s to obtain the p.g.f. of X +Y. What is then the distribution of X+Y?