Problem 9:
Consider a random variable \( X \) with density function
\[
f_{X}(x)=\left\{\begin{array}{ll}
\frac{18}{x^{3}}, & \text { for } x \geq 3 \\
0, & \text { otherwise }
\end{array}\right.
\]
i) Apply Chebyshev's inequality to find the bound for the probability \( P(X \geq 5) \).
ii) Determine the value of \( a \in \mathbb{R} \) such that \( P(X \geq a) \leq 0.05 \).
iii) In case \( E(X) \) exists, compute this value.
iv) In case \( \operatorname{Var}(X) \) exists, compute this value.
