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Let X1, X2, X3, and X4 be mutually independent random variables from the same distribution. Let...

Let X1, X2, X3, and X4 be mutually independent random variables from the same distribution. Let
S = X1 + X2 + X3 + X4. Suppose we know that S is a Chi-Square random variable with 2 degrees of freedom. What
is the distribution of each of the Xi?

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