Math puzzle: Breaking the camel's back.

[pzhon]

Here is a problem and two generalizations. Part 1 is a well-known problem which is nontrivial, but solvable by several techniques. I solved it over dinner as a kid. Part 2 is less well-known. The solution I've seen published is overly complicated, but a simple solution is possible, and generalizes to Part 3.

Part 1: Your camel's back can hold 1 unit. Straws have weights which are uniformly distributed from 0 to 1 unit, and independent of each other. You add one straw at a time. If the weights are 0.7, 0.1, 0.8..., then your camel's back breaks on the 3rd straw. On average, how many straws does it take to break your camel's back?

Part 2: Let f(x) be the average number of straws it takes to break a camel's back if it can hold x units. Determine the asymptotics of f up to o(1), i.e., produce a simple function g so that the limit of f(x)-g(x) as x->infinity is 0.

Part 3: Produce a method for determining the asymptotics for some more general continuous weight distributions, such as the square of a uniformly distributed random variable, or the sum of two.

If you have a nice solution to only 1 part, it is worth posting it, but please put solutions in white.