Question

Let X1 d= R(0,1) and X2 d= Bernoulli(1/3) be two independent random variables, define Y :=...

  1. Let X1 d= R(0,1) and X2 d= Bernoulli(1/3) be two independent random variables, define Y := X1 + X2 and U := X1X2.

    1. (a) Find the state space of Y and derive the cdf FY and pdf fY of Y .
      (You may wish to use {X2 = i}, i = 0,1, as a partition and apply the total probability formula.)

    2. (b) Compute the mean and variance of Y in two different ways, one is through the pdf of Y and the other is using the sum of two independent random variables.

    3. (c) Calculate E(U) and V(U).

    4. (d) Find the state space of U and calculate the cdf FU of U.

    5. (e) Calculate Cov(U, X2) and ρ(U, X2).

0 0
Add a comment Improve this question Transcribed image text
Answer #1

Tial 3 2. 3 ナ(y-1 3 3 0 23 41 3 2- 5 2- 3 3 36 3612 3 3 363 их 1 618e@x):eer (U, X2 o.gl ‘ ף9 7 _-- : 42 12 a 0,2

Add a comment
Know the answer?
Add Answer to:
Let X1 d= R(0,1) and X2 d= Bernoulli(1/3) be two independent random variables, define Y :=...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT