# Homework Assignment #5

## Statistics 220, Fall 2005

Due October 5
Show your work! Partial credit will be given on the basis of your work;
writing down the answer without showing your work will get you no credit.

**Non-Devore problem**: Plutonium-239 is one of the substances
used to make atomic (fission) bombs. It is radioactive, and the half-life is
24,110 years. That is, the probability that any given atom of plutonium has
decayed after 24,110 years is exactly 0.5.

(a) Assuming that the probability of decay follows an exponential
distribution, what is the rate of decay? (*Hint*: Set up an equation
with the CDF and solve for the rate.)

(b) What is the probability that an atom will decay within one year?
(*Hint:* for small x, exp(-x) is approximately 1-x.)

(c) A critical mass of plutonium is 10 kilograms. Each kilogram contains
2.5*10^24 atoms of plutonium. Approximately how many atoms do you expect to
have decay in one year from a critical mass of plutonium? (You can assume that
whether or not any one atom decays is independent of what all the other atoms
do.)

Problems from Devore:

- Exercise 4.5. (Hint: Find the CDF, and use that in parts (b), (c) and
(d).)
- Exercise 4.12, only parts (a), (b), and (c).
- Exercise 4.27.
- Exercise 4.30.
- Exercise 4.31.
- Exercise 4.41.
- Exercise 4.47.
- Exercise 4.60.
- Exercise 4.63.