**Homework assignment #3**

Complete exercises 3.1 and 3.9 in Bevington. The questions are reproduced below in case you don't have the book.

**3.1 (3.1)**: Find the uncertainty in
x as a function of the uncertainties in u and v for the following functions.
This question should be answered in analytical form. Show your work. You may
assume that u and v are completely uncorrelated. If you find it to be more convenient,
you may express your result as a relative error in x (i.e. sigma_x/x).

a) x = 1/[2(u+v)]

b) x = 1/[2(u-v)]

c) x = 1/u^2

d) x = u v^2

e) x = u^2 + v^2

**3.2 (3.9): ** 100 Students in an undergraduate
laboratory recorded the following counts in 1-min intervals from a radioactive
source. The nominal mean decay rate of the source is 3.7 decays per minute.

The students' data is available here in text or Excel formats. Column 1 is "decays per minute", column 2 is "frequency of occurrence", the number of times that number of decays per minute was observed.

** a)** Find
the mean decay rate and its standard deviation. Compare the
standard
deviation of the value expected from the Poisson distribution for the
mean
value that you obtained.

** b)** Plot
a histogram of the data and show Poisson curves of both the parent and
the observed distributions.

You may use whatever software is
available
to you to answer this question, but outline your reasoning in complete
sentences. You may also wish to refer to section 2.2 of Bevington
for a discussion of the Poisson distribution. Taylor discusses Poisson
distributions in chapt 11.