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
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
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
Can someone please answer?
other answers please
Can anyone please aswer the rest of the part??? I would be very gradeful
if anyone can
provide the other answers .....