Find $E[X_1|X_1 + \cdots +X_n=x] $
This is pretty new concept for me so any help would be very helpful.
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https://math.stackexchange.com/questions/78546/conditional-expectation-for-a-sum-of-iid-random-variables-e-xi-mid-xi-eta-e – Jun 02 '17 at 05:20
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You need to assume that $X_1$ is integrable and this fact should be stated in the assumption. – Danny Pak-Keung Chan Aug 07 '17 at 16:43
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Hint:
$$\mathbb{E}[X_i|\sum_{k=1}^n X_k=x]= \mathbb{E}[X_j|\sum_{k=1}^n X_k=x]$$
You might want to use linearity of expectation and sum of $n$ copies of them for a start.
Siong Thye Goh
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Maybe nitpicking here, but did you on purpose not write '$X_k$' in the sum? :) nice hint btw – Blaza Jun 01 '17 at 21:50
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