Tail Probability and Conditional Expectation of the Pareto Distribution

The Pareto distribution with shape $\alpha > 0$ and scale $x_m > 0$ has PDF $$f(x) = \frac{\alpha\, x_m^\alpha}{x^{\alpha+1}}, \quad x \geq x_m.$$

(a) Derive $P(X > t)$ for $t \geq x_m$.

(b) Derive $E[X \mid X > t]$ for $\alpha > 1$ and $t \geq x_m$.

(c) Compute both quantities for $\alpha = 3$, $x_m = 1$, $t = 2$.