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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).

  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.

  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


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    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


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    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?
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