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Suppose that Y and Y, has a joint density function given by 0 < y1 < Y2 < 1, C, f(y1, Y2) = 0, elsewhere. (a) Find the probability density function for U = Y1 + Y2. (b) Evaluate E[U].

Suppose that Y and Y, has a joint density function given by 0 < y1 < Y2 < 1, C, f(y1, Y2) = 0, elsewhere. (a) Find the probability density function for U = Y1 + Y2. (b) Evaluate E[U].

MATLAB: An Introduction with Applications
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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Please answer both parts of Question 1, part a and part b. Show all work and all steps.

* For part a of this problem, please follow the similar approach attached below as "Problem 1 Method." Your work for part a should be similar to the "Problem 1 Method" picture, but it should be rewritten to account for the numbers in problem 1. **

Part b can be solved normally.

 

 

1. Suppose that Y1 and Y2 has a joint density function given by 0< y1 < Y2 < 1, C, f (y1, 42) = 0, elsewhere. (a) Find the probability density function for U = Y1 +Y2. (b) Evaluate E[U].
Transcribed Image Text:1. Suppose that Y1 and Y2 has a joint density function given by 0< y1 < Y2 < 1, C, f (y1, 42) = 0, elsewhere. (a) Find the probability density function for U = Y1 +Y2. (b) Evaluate E[U].
Soln: Check Bounday: 0<U=Y,+Y2 < 2 Need to find Fu (w) = P(U sw) =P CY + Yz su)= J] fly,, Ye) dy, dyz D if u<o, Fu lu) = Sf o dg, d% 9 if icusz. Fu lu) = |- ST" 1 dy, dyz =1- u-2 - u2 +2u -| u<o DF: Fu lu) = u/2 PDF: fu cu)= dlulu)_| 2-u i<usz du osu El PDF: fulw)= 2-u I<Us -4/2 + 2u-1 1 O. w. ル>)
Transcribed Image Text:Soln: Check Bounday: 0<U=Y,+Y2 < 2 Need to find Fu (w) = P(U sw) =P CY + Yz su)= J] fly,, Ye) dy, dyz D if u<o, Fu lu) = Sf o dg, d% 9 if icusz. Fu lu) = |- ST" 1 dy, dyz =1- u-2 - u2 +2u -| u<o DF: Fu lu) = u/2 PDF: fu cu)= dlulu)_| 2-u i<usz du osu El PDF: fulw)= 2-u I<Us -4/2 + 2u-1 1 O. w. ル>)
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