Probability

Let X and Y be jointly continuous nonnegative random variables. A particular value y of Y is observed and it turns out that fX|Y(x∣y)=2e−2x , for x≥0 .

Find the LMS estimate (conditional expectation) of X .
unanswered

Find the conditional mean squared error E[(X−XˆLMS)2∣Y=y] .
unanswered

Find the MAP estimate of X .
unanswered

Find the conditional mean squared error E[(X−XˆMAP)2∣Y=y] .
unanswered

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  2. 👎
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  4. ℹ️
  5. 🚩
  1. a) 1/2
    b) 1/4
    c) 0
    d) 1/2

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    2. 👎
    3. ℹ️
    4. 🚩
  2. Can you show your calculations for a)?

    I got a different result: 1/4

    E[X|Y=y] = integral x*fX|Y(x|y)dx
    = integral(infinity to 0) x*2e^(-2x) dx
    =1/4

    Am i wrong here?

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