Homework 10: Continuous Random Variables

1. Section 3.2, #4, 5, 6, 8.
2. Let \(X\) be the lifetime of a certain electronic device (measured in hours). Suppose that the probability density function of \(X\) is given by $$ f_X(x)= \begin{cases} \frac{10}{x^2}, & x>10\\ 0, & x\leq 10 \end{cases} $$
   1. Find \(P(X>20)\).
   2. What is the probability that of 6 such devices, at least 3 will function for at least 20 hours? What assumptions are you making?