# 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)'.

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.

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.

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.

1. 👍 1
2. 👎 0
3. 👁 4,334

1. 👍 0
2. 👎 0
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

1. 👍 8
2. 👎 0

1. 👍 0
2. 👎 0
4. Can anyone please aswer the rest of the part??? I would be very gradeful

1. 👍 0
2. 👎 0
5. if anyone can

1. 👍 0
2. 👎 0
6. can anyone provides the answer

1. 👍 0
2. 👎 0
7. 1. 1/(2*theta*ln(x/2))
2. x/2
3. (1-x/2)/(2*ln(x/2))

1. 👍 2
2. 👎 6
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

1. 👍 15
2. 👎 1
9. Thanks, REV

1. 👍 1
2. 👎 1
10. Thanks a lot REV

1. 👍 0
2. 👎 1
11. Thank you so much REV

1. 👍 0
2. 👎 1

## Similar Questions

1. ### math

We are given a stick that extends from 0 to x . Its length, x , is the realization of an exponential random variable X , with mean 1 . We break that stick at a point Y that is uniformly distributed over the interval [0,x] . 1.

2. ### Probability

Let Θ be a Bernoulli random variable that indicates which one of two hypotheses is true, and let P(Θ=1)=p. Under the hypothesis Θ=0, the random variable X is uniformly distributed over the interval [0,1]. Under the alternative

3. ### probability; math

Let X be a continuous random variable. We know that it takes values between 0 and 6 , but we do not know its distribution or its mean and variance, although we know that its variance is at most 4 . We are interested in estimating

4. ### Probability

We are given a stick that extends from 0 to x . Its length, x , is the realization of an exponential random variable X , with mean 1 . We break that stick at a point Y that is uniformly distributed over the interval [0,x] . Find

1. ### Math

Searches related to The random variables X1,X2,…,Xn are continuous, independent, and distributed according to the Erlang PDF fX(x)=λ3x2e−λx2, for x≥0, where λ is an unknown parameter. Find the maximum likelihood estimate

2. ### probability

We are given a stick that extends from 0 to x . Its length, x , is the realization of an exponential random variable X , with mean 1 . We break that stick at a point Y that is uniformly distributed over the interval [0,x] . 1.

3. ### Probability

Confidence interval interpretation Every day, I try to estimate an unknown parameter using a fresh data set. I look at the data and then I use some formulas to calculate a 70% confidence interval, [Θˆ−,Θˆ+], based on the

4. ### math, probability

13. Exercise: Convergence in probability: a) Suppose that Xn is an exponential random variable with parameter lambda = n. Does the sequence {Xn} converge in probability? b) Suppose that Xn is an exponential random variable with

1. ### Probability

A simple CI Let θ be an unknown parameter, and let X be uniform on the interval [θ−0.5,θ+0.5]. Is [X−2,X+2] an 80% confidence interval? unanswered I form a confidence interval of the form [X−a,X+a]. What is the narrowest

2. ### Probability

Let K be a Poisson random variable with parameter λ : its PMF is pK(k;λ)=λke−λk!,for k=0,1,2,…. What is the ML estimate of λ based on a single observation K=k ? (Your answer should be an algebraic function of k using

3. ### Probability

Let Θ be an unknown random variable that we wish to estimate. It has a prior distribution with mean 1 and variance 2. Let W be a noise term, another unknown random variable with mean 3 and variance 5. Assume that Θ and W are

4. ### probability

Consider a Bernoulli process with parameter p=1/3. Let T1 be the time of the first success and let T1+T2 be the time of the second success. We are told that the results of the two slots that follow the first success are failures,