Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Libniz

  • 2 years ago

The input X to a binary communication channel assumes the values +1 or −1 with probabilities 1/3 and 2/3 respectively. The output Y of the AWGN channel is given by Y = X + N where N is zero mean Gaussian noise with variance 2 n = 1. 1. Find the conditional pdf of Y given X = +1.

  • This Question is Closed
  1. Libniz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @phi

  2. Libniz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so obiviously Y=X+N X being 1 Y=1+N Y=1+N N being \[\phi(x-\mu/1)\] \[\phi(x-0/1)\] \[\phi(1-0/1)\]=\[\phi(1)\] we add to 1 on top so \[\phi(1)+1\] and divde by conditional probability 1/3

  3. phi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I have not looked at this stuff, but my intuition is that if x is given as 1, the pdf for y should look like N, but centered at 1 (a gaussian with 1 mean, variance 2)

  4. phi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I'll put this subject on my "to do" list. In the meantime....

  5. JakeV8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I think @phi is correct. As long as X is given as 1, then the probability of x occurring doesn't affect the pdf.

  6. JakeV8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    A more interesting (read: "hard") pdf is the overall pdf that encompasses both x = 1 and x = -1. Thankfully, that wasn't the question :)

  7. JakeV8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    my "to do" list seems to grow with every day I sign on here... (sigh)

  8. Libniz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    "then the probability of x occurring doesn't affect the pdf." can you explain why?

  9. Libniz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @satellite73

  10. JakeV8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I thought of it just like simple conditional probability... if P(x) = 0.5 and P(y) = 0.3, but the problem says, "Given x, what is the probability of y?", then the P(x) doesn't affect the probability of P(x|y), since you know x is given. Here, the fact that x = 1 occurs 1/3 of the time is irrelevant to the pdf if you are given that x = 1.

  11. Jessica_Moore
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    https://onlinecourses.science.psu.edu/stat414/book/export/html/95 This site might help you with Conditional Distributions. It might help you.

  12. Libniz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thank you so much for not ignoring my question

  13. Jessica_Moore
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Your welcome. anytime.

  14. Libniz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks to jessica as well

  15. JakeV8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So, I think if you run "x = 1" through the channel, then you would expect Y to look like 1, but it would have the shape of the pdf of the AWGN due to the channel. But the signal X = 1 would move the mean to be around 1 vs. around 0 which is what the channel looks like with no signal.

  16. JakeV8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    My comment earlier about the overall pdf was if you were trying to build a sensor/detector, and you didn't know whether X was +1 or -1, and you picked up an output signal Y = 0.2, you would have to decide if it was really an X= -1 input or if it was an X = + 1 input... the conditional pdfs would be overlapping.

  17. Libniz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok,

  18. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.