• Support PF! Buy your school textbooks, materials and every day products Here!

Proof of expected value expression

  • Thread starter grimster
  • Start date
  • #1
39
0
The usual expression of the expected value of X is:
E[X] = (sum) x*p(x)

i'm supposed to show that, for X a random non-negative discrete random(stochastic) variable, we have that:
E[X]=(sum: i from 1 to infinity) P(X>=i)

i have absolutely no idea how to do this. does anyone want to push me in the right direction?
 

Answers and Replies

  • #2
mathman
Science Advisor
7,819
433
P(X>=i)=sum(j=i,inf) P(X=j). Plug this into your sum over i, interchange i and j and you will get what you want, since the sum over i will simply be j.
 

Related Threads on Proof of expected value expression

  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
0
Views
4K
Replies
5
Views
497
Replies
18
Views
3K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
2
Views
7K
  • Last Post
Replies
2
Views
3K
Replies
6
Views
1K
Top