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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

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For i.i.d X and Y , if X + Y and X - Y are independent, show X is normally distributed [closed]

The question goes as follows: If $X$ and $Y$ are independent and identically distributed, their density function $f(x)$ is strictly positive and second-order continuously differentiable. If $X+Y$ and …
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