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Thread: Binomial expectation E(X|X>1)

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    Red face Binomial expectation E(X|X>1)




    General case: X~B(n,p)
    I could integrate the product of x and pmf from 1 to infinity and divide it by the integral of just pmf from 1 to infinity to find it, but I'm really stuck since I can't do it due to the sophisticated pmf function of binomial.
    How can we find this expectation and Variance(X|X>1)?
    Thank u💕

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    Re: Binomial expectation E(X|X>1)


    Seeing it's binomial, it is a sum to n terms, rather than an integral to infinity. Imagine the full probability table. Each x has a p, xp and x^2p. From these you can work out mean = sum of xp, and var = sum of x^2p - mean^2.
    Now we have x = 0 and x = 1 removed. For x=0 the xp and x^2p were 0 and 0, Find the values for xp and x^2p for x = 1. Find the new sum of xp and sum of x^2p and so your new mean and variance.

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