(Solution Library) [2 + 4 + 4 = 10 pts] The random variable X has PDF f(x)= cx^-3 1≤ x≤ 3 , 0 elsewhere
Question: [2 + 4 + 4 = 10 pts] The random variable X has PDF
\[f\left( x \right)=\left\{ \begin{aligned} & c{{x}^{-3}}\text{ }1\le x\le 3 \\ & 0\text{ elsewhere} \\ \end{aligned} \right.\]- Find the value of c and P(X < 2).
- Find the conditional PDF and mean of X given that X < 2.
- Let \(Y={{X}^{2}}\). Find conditional mean and variance of Y given X < 2.
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