1. A string of 10 light bulbs is connected in parallel, which means that the entire string will fail to light up only if all 10 of the light bulbs fail. Assume that the lifetimes of the bulbs, τ1,..., τ10, are independent random variables that are exponentially distributed with mean θ. Find the distribution of the lifetimes of this string of light bulbs.
2. Let X1,..., Xn be a random sample from the uniform distribution f(x) = 1/2, 0 ≤ x ≤ 2. Find the probability density function for the range R = (X(n) - X(1)).