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...


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<br>0< y1 < Y2 < 1,<br>C,<br>f (y1, 42) =<br>0,<br>elsewhere.<br>(a) Find the probability density function for U = Y1 +Y2.<br>(b) Evaluate E[U].<br>

Extracted 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="">
Soln: Check Bounday: 0<U=Y,+Y2 < 2<br>Need to find Fu (w) = P(U sw) =P CY + Yz su)= J] fly,, Ye) dy, dyz<br>D if u<o, Fu lu) = Sf o dg, d%<br>9 if icusz. Fu lu) = |- ST) "/>
Extracted text: Soln: Check Bounday: 0)

Jun 11, 2022
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