# 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 .

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

Find the MAP estimate of X .

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

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
1. a) 1/2
b) 1/4
c) 0
d) 1/2

1. 👍
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?

1. 👍
2. 👎
3. ℹ️
4. 🚩

## Similar Questions

1. ### probability

Problem 4. Gaussian Random Variables Let X be a standard normal random variable. Let Y be a continuous random variable such that fY|X(y|x)=12π−−√exp(−(y+2x)22). Find E[Y|X=x] (as a function of x , in standard notation)

2. ### Probability

Events related to the Poisson process can be often described in two equivalent ways: in terms of numbers of arrivals during certain intervals or in terms of arrival times. The first description involves discrete random variables,

3. ### probability

For each of the following sequences, determine the value to which it converges in probability. (a) Let X1,X2,… be independent continuous random variables, each uniformly distributed between −1 and 1. Let

4. ### Statistics

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 . 1. Find the LMS estimate (conditional expectation) of X . 2. Find the

1. ### probability

Problem 2. Continuous Random Variables 2 points possible (graded, results hidden) Let 𝑋 and 𝑌 be independent continuous random variables that are uniformly distributed on (0,1) . Let 𝐻=(𝑋+2)𝑌 . Find the probability

2. ### Math

For the discrete random variable X, the probability distribution is given by P(X=x)= kx x=1,2,3,4,5 =k(10-x) x=6,7,8,9 Find the value of the constant k E(X) I am lost , it is the bonus question in my homework on random variables

3. ### Statistics

Let X1,X2,…,Xn be i.i.d. random variables with mean μ and variance σ2 . Denote the sample mean by X¯¯¯¯n=∑ni=1Xin . Assume that n is large enough that the central limit theorem (clt) holds. Find a random variable Z with

4. ### Probability

Let X be a continuous random variable, uniformly distributed on some interval, and let Y = aX + b. The random variable will be a continuous random variable with a uniform distribution if and only if (choose one of the following

1. ### Probability

1.Let 𝑋 and 𝑌 be two binomial random variables: a.If 𝑋 and 𝑌 are independent, then 𝑋+𝑌 is also a binomial random variable b.If 𝑋 and 𝑌 have the same parameters, 𝑛 and 𝑝 , then 𝑋+𝑌 is a binomial

2. ### Statistics

Z1,Z2,…,Zn,… is a sequence of random variables that converge in distribution to another random variable Z ; Y1,Y2,…,Yn,… is a sequence of random variables each of which takes value in the interval (0,1) , and which

3. ### linear algebra

Let V be the set of all real-valued continuous functions defined on R1. If f and g are in V, we define f ⊕ g by (f ⊕ g)(t) = f(t) + g(t). If f is in V and c is a scalar, we define c f by (c f)(t) = cf(t). Then V is a vector