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Thread: theoretical exercises about probability problems

  1. #1
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    theoretical exercises about probability problems

    Let X1,...,Xn be independent and identically distributed random variables. Find

    E[X1|X1+...+Xn=x]
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  2. #2
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    Re: theoretical exercises about probability problems

    I believe it will be
    $\dfrac{x}{n}$
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  3. #3
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    Re: theoretical exercises about probability problems

    $\displaystyle \sum_{k=1}^n~E[X_k | X_1 + \dots +X_n = x] = x$

    $E[X_1 | X_k + \dots +X_n = x] = E[X_k | X_1 + \dots +X_n = x],~\forall k \in [1,n]$

    Thus

    $E[X_1 | X_k + \dots +X_n = x] = \dfrac x n$
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