Question: 2.11. (Sec. 2.3) Suppose the scalar random variables XI' Xn are independent and have a density which is a function only of x? + ...

2.11. (Sec. 2.3) Suppose the scalar random variables XI"'" Xn are· independent and have a density which is a function only of x? + ... +x;. Prove that the Xi are normally distributed with mean 0 and common variance. Indicate the mildest conditions on the density for your proof.

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