Probability

The random variable X is uniformly distributed over the interval [θ,2θ]. The parameter θ is unknown and is modeled as the value of a continuous random variable Θ, uniformly distributed between zero and one.

Given an observation x of X, find the posterior distribution of Θ. Express your answers below in terms of θ and x. Use ‘theta' to denote θ and ‘ln' to denote the natural logarithm function. For example, ln(θ) should be entered as ‘ln(theta)'.

For 0≤x≤1 and x/2≤θ≤x,fΘ∣X(θ∣x)=- unanswered
Find the MAP estimate of Θ based on the observation X=x and assuming that 0≤x≤1. Express your answer in terms of x.

For 0≤x≤1,θ^MAP(x)= - unanswered
Find the LMS estimate of Θ based on the observation X=x and assuming that 0≤x≤1. Express your answer in terms of x.

For 0≤x≤1,θ^LMS(x)=- unanswered
Find the linear LMS estimate θ^LLMS of Θ based on the observation X=x. Specifically, θ^LLMS is of the form c1+c2x. Find c1 and c2.

c1= - unanswered
c2= - unanswered

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  1. Can someone please answer?

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  2. 2. Find the MAP estimate of Θ based on the observation X=x and assuming that 0≤x≤1. Express your answer in terms of x.

    For 0≤x≤1,θ^MAP(x)= x/2

    PLEASE, if you are bugged with this problem set. Do not be mean and provide the other answers

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  3. other answers please

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  4. Can anyone please aswer the rest of the part??? I would be very gradeful

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  5. if anyone can
    provide the other answers .....

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  6. can anyone provides the answer

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  7. 1. 1/(2*theta*ln(x/2))
    2. x/2
    3. (1-x/2)/(2*ln(x/2))

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  8. The above answers are wrong, here is the official indictment:

    1. 1/(theta*ln(2))

    3. x/(2*ln(2))

    4 .

    c1= 0.06452

    c2= 0.58065

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  9. Thanks, REV

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  10. Thanks a lot REV

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  11. Thank you so much REV

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