Can I do expectation like this

  • Thread starter aegea
  • Start date
  • #1
2
0
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!
 

Answers and Replies

  • #2
4
0
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]
 
Last edited:

Related Threads on Can I do expectation like this

Replies
2
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
5
Views
2K
Replies
9
Views
2K
Replies
3
Views
957
  • Last Post
Replies
5
Views
772
B
Replies
17
Views
3K
Replies
2
Views
958
Replies
2
Views
726
Top