1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Random variables

  1. Apr 29, 2008 #1
    a discrete random variable has range space {1, 2, ..., n} and satisfies P(X=j) = j/c for some number c. Find c, and then find E(X), E(X^2), E(1/X) and Var(X).

    thanks
     
  2. jcsd
  3. Apr 29, 2008 #2
    What is your solution?

    You have the probability mass function (pmf). You can determine the constant c.

    The expectations are obtained directly by definition...
     
  4. Apr 29, 2008 #3
    Thanks for your reply.

    Sorry I should have stated before that I don't know where to start on this.

    I just looked up on pmf, and I have no examples on a question like this in my notes.

    The 'j' confuses me in the question as I don't see how it relates to anything else, so finding c is tricky for me.

    Thanks
     
  5. Apr 29, 2008 #4
    Well, aren't there a few conditions that all valid pmf's are required to satisfy? It would probably be a good idea to review these.

    j is simply a dummy variable. Just shorthand for saying P(X=1) = 1/c, P(X=2) = 2/c, ..., P(X=n) = n/c.

    Perhaps this thread should be moved to the homework help section?
     
  6. Apr 29, 2008 #5
    The conditions I know of pmf are that the total sum of the probabilities from -infinity to infinity is 1, and the probabilities can only take values between 0 and 1.

    So do I have to find a j/c which has a sum of the series from -infinity to infinity equal to 1?

    Sorry I'm really confused..

    ok so I have so far:

    1/c + 2/c + 3/c ... +n/c = 1

    1 + 2 + 3 +.. + n = c

    c = infinity?
     
  7. Apr 29, 2008 #6

    exk

    User Avatar

    a pmf is for a discrete random variable.

    Do you know what the definition of a discrete RV is?

    Otherwise you have the right idea. c doesn't have to equal infinity. what is the sum of n consecutive integers?
     
  8. May 2, 2008 #7

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    No, only 1 to n, the number over which your probability distribution is defined.

    Why should it be? n is a fixed finite number, not "infinity". Do you know the formula for the sum of the first n positive integers?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Random variables
  1. Random variables (Replies: 2)

  2. Random variable (Replies: 2)

  3. Random Variable (Replies: 1)

  4. Random variable (Replies: 1)

Loading...