Explore BrainMass

Explore BrainMass

    Estimation : Binomial Distribution

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Suppose T is a random variable such that

    P(T=k) = (k-1)C(r-1) * p^r * (1-p)^(k-r)

    (It is a negative binomial distribution.).

    I am trying to find the expected value


    (which is equal to r * E(1/T))

    By (k-1)C(r-1) I mean (k-1)!/[(r-1)!*(k-r)!].

    © BrainMass Inc. brainmass.com November 24, 2022, 11:36 am ad1c9bdddf

    Solution Preview

    It is a well know theorem that the expectation operator E(X) has the following properties:

    (a) if X ≥ 0, then E(X) ≥ 0,
    (b) if a,b are real, then E(aX+bY)=aE(X)+bE(Y), ...

    Solution Summary

    The expected value is calculated. Binomial distribution estimation is calculated for a function.