Register to reply

Can I do expectation like this

by aegea
Tags: expectation
Share this thread:
aegea
#1
Mar4-10, 10:23 AM
P: 2
Many thanks in advance

Suppose x is normal variable x~N(a,b)
and y=160*x^2
I need calculate E(y)=∫yf(y)d(y)
f(y) is the density function of y
how can I write it as an integral of x since we know x's distribution, I mean use the density function of x to substitute the original integral

Can I just use E(y)=E(160 x^2)= ∫ 160 x^2 f(x) d(x)
then I can use f(x), which is the density function of normal.

Seems right, but seems wrong, seems I use f(x) to substitute x directly!
Phys.Org News Partner Science news on Phys.org
World's largest solar boat on Greek prehistoric mission
Google searches hold key to future market crashes
Mineral magic? Common mineral capable of making and breaking bonds
dyrich
#2
Mar4-10, 09:12 PM
P: 4
You can do it the way you suggested (it is logically correct), but I believe it will make more work for yourself (but I didn't look at it because there is a cleaner way).

Here are a few hints that should help:

Remember that the expected value function is a linear operator so

[tex] E(Y)=E(160X^2)=160E(X^2) [/tex]

and

[tex] V(X)=E(X^2)-[E(X)]^2 [/tex]


Register to reply

Related Discussions
Expectation value of p^2 Advanced Physics Homework 10
Expectation Value Calculus & Beyond Homework 4
The Expectation of X and the Expectation of X squared (discrete math) Calculus & Beyond Homework 2
Expectation value Calculus & Beyond Homework 9
Expectation Value Advanced Physics Homework 5