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A random variable or stochastic variable is a value that is subject to chance variation (i.e., randomness in a mathematical sense).
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joint PDF of continuous and discrete random variables
Given exponential a random distribution X with PDF $f_X(x)=\lambda e^{-\lambda x}$ and a random variable Z with the PMF $p_Z[z]=0.5, z= \pm1$, I am trying to find the PDF of $Y=ZX$ (I also know that Z …