(Step-by-Step) Let the continuous random variable X have the following PDF.
Question: Let the continuous random variable \(X\) have the following PDF.
\[f(x)=\left\{\begin{array}{cc} \lambda^{2} \cdot x \cdot e^{-\lambda x}, \quad x \geq 0 \\ 0 \quad \text { otherwise } \end{array} \quad \text { for some } \lambda>0\right.\]- Verify that this does define a PDF.
- Find \(\mathrm{E}(\mathrm{X})\).
- Find \(\operatorname{Var}(\mathrm{X})\).
Hint: use integration by parts
Deliverable: Word Document 
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