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In this blog post, we’ll explore the connections among conditional mean, variance, conditional Probability Density Functions (PDFs), and also its relationship with Minimum Mean Square Error (MMSE) estimator. Conditional Probability Density Function Consider two random variables, $X$ and $Y$ (which could be complex).

In this article, we’ll delve into the expressions for the density function of the sum of independent exponential random variables. Additionally, we’ll explore an application involving the probability density function (PDF) of the norm square of a correlated Gaussian random vector.

In this article, we explore the computation of the probability density function (PDF) for the sum of independent Exponential and Gaussian random variables. Let’s consider $Y$, the sum of independent $X$ (Exponential) and $N$ (Gaussian) random variables: