Uniform distribution find E(Y|x)

In summary, the question is asking for the expected value of Y given that X and Y have a uniform distribution over the circle x^2 + y^2 \leq 9. The hint given is to use an integral with respect to y, as x is fixed. The possible range for y is between -\sqrt{9- x^2} and \sqrt{9- x^2}, and the final answer for E(y|x) will be a function of x.
  • #1
confused88
22
0
This is the question:

If X and Y have a uniform distribution over the circle x^2 + y^2 [tex]\leq[/tex] 9 find E(Y|x).

Can someone please explain to me, how to answer this question. You guys don't have to give me a solution, but a hint would be nice because I have no idea where to start. Thank you :smile:
 
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  • #2
well what i was thinking was that the range is between 3 and 0 and -3 and 0.

Then you integrate x^2 + y^2 with the first range (3 and 0) and then with -3 and 0. Is this right?

Or is the first range y to 3, and then -3 to 0?

I have no idea, please help me
 
  • #3
"E(y|x)" means the mean value of y for a single value of x. There will only be an integral with respect to y, not x. x is fixed. y ranges between [itex]-\sqrt{9- x^2}[/itex] and [itex]\sqrt{9- x^2}[/itex]. Your final answer for E(y|x) will be a function of x.
 
  • #4
Thank you for replying. Yupp I think that i got the answer. I got zero at the end, but I'm pretty sure that's right
 

FAQ: Uniform distribution find E(Y|x)

1. What is the definition of "Uniform distribution find E(Y|x)"?

The uniform distribution is a probability distribution where all outcomes are equally likely. E(Y|x) refers to the expected value of the variable Y given a specific value of x.

2. How is the expected value calculated for a uniform distribution?

The expected value for a uniform distribution is calculated by taking the average of all possible outcomes. In other words, it is the sum of all outcomes divided by the total number of outcomes.

3. What does the expected value represent in a uniform distribution?

The expected value in a uniform distribution represents the long-term average outcome. In other words, if the experiment is repeated many times, the expected value is the value that is most likely to occur.

4. Can the expected value be negative in a uniform distribution?

No, the expected value cannot be negative in a uniform distribution. Since all outcomes are equally likely, the average of all outcomes will always be a positive number.

5. How does the uniform distribution differ from other probability distributions?

The uniform distribution differs from other probability distributions in that it has a constant probability for all outcomes, whereas other distributions may have varying probabilities for different outcomes. Additionally, the expected value for a uniform distribution is always in the center of the distribution, while for other distributions it may be shifted to one side or the other.

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