subject
Mathematics, 06.04.2021 04:40 Arealbot

Let Y = X + N, where X is the input, N is the noise, and Y is the output of a system. Assume that X and N are independent random variables. It is given that E[X] = 0, Var[X] = σ 2 X, E[N] = 0, Var[N] = σ 2 N . (a) Find the correlation coefficient rho between the input X and the output Y . (b) Suppose we estimate the input X by a linear function g(Y ) = aY . Find the value of a that minimizes the mean squared error E[(X − aY ) 2 ]. (c) Express the resulting mean squared error in terms of η = σ 2 X/σ2 N .

ansver
Answers: 2

Other questions on the subject: Mathematics

image
Mathematics, 21.06.2019 16:00, angellynn50
Write two subtraction equations that are equivalent to 5 + 12 = 17.
Answers: 3
image
Mathematics, 21.06.2019 20:30, erikloza12pdidtx
Jose is going to use a random number generator 500500 times. each time he uses it, he will get a 1, 2, 3,1,2,3, or 44.
Answers: 1
image
Mathematics, 21.06.2019 21:30, iamhayls
Mama mia restaurant used 1 2 2 1 ? of their mozzarella cheese making pizza and the remaining 6 4 64 ounces making pasta. how many pounds of mozzarella cheese did mama mia start with?
Answers: 1
image
Mathematics, 21.06.2019 23:00, britann4256
Calculate the average rate of change over the interval [1, 3] for the following function. f(x)=4(5)^x a. -260 b. 260 c. 240 d. -240
Answers: 1
You know the right answer?
Let Y = X + N, where X is the input, N is the noise, and Y is the output of a system. Assume that X...

Questions in other subjects:

Konu
Mathematics, 15.01.2021 18:40