Let X and Y be two independent normally distributed random variables with expected value 0 and variance 1. Find their joint PDF. Plot its level curves.
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We know that X and Y are independent normally distributed random variables with expected value 0 and variance 1. So, their individual probability density functions (PDFs) are given by: $$ f_X(x) = \frac{1}{\sqrt{2\pi}} e^{-\frac{x^2}{2}} \quad \text{and} \quad Show more…
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