[Solved] The random variable X has the pdf: f_X(x)=(1)/(2 β) e^-|x-α| / β \text for -∞0 Find the cumulative distribution function
Question: The random variable \(X\) has the pdf:
\[f_{X}(x)=\frac{1}{2 \beta} e^{-|x-\alpha| / \beta} \text { for }-\infty- Find the cumulative distribution function \(F_{X}(x) .\)
- Find \(M_{X}(t)\), the moment generating function for \(X\). Provide bounds for \(t\) to receive full credit.
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Find \(G_{X}(t)\), the factorial moment generating function for \(X\). Provide bounds for \(t\) to receive full credit.
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