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.

Question

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

Answer 1

Can someone please answer?

Answer 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

Answer 3

other answers please

Answer 4

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

Answer 5

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

Answer 6

can anyone provides the answer

Answer 7

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

Answer 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

Answer 9

Thanks, REV

Answer 10

Thanks a lot REV

Answer 11

Thank you so much REV