The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Math Topics » discretemath

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Proof convergence
Replies: 1   Last Post: Mar 20, 2010 12:03 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 1
Registered: 3/20/10
Proof convergence
Posted: Mar 20, 2010 10:25 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


I have problems with a proof I should show.
I should show that, given X a r.v. >=0, then the expected value E(X)<inf iff sum_(i>=1)P(X>i)<inf.

I tried out different way, but I don't get how to solve this problem.
Starting from the expected value formula, I get stuck already at sum_(i>=1)(P(x=i)*i)<inf (don't knowing how to proceed).
If I start at the other side, I get (for descrete n):

I really don't know how I can proof this statement, even though I do understand its meaning...

Please help me,

Thanks in advance :)

Date Subject Author
Read Proof convergence
Read RE: Proof convergence
Ben Brink

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.