Homework assignment #2
Complete exercises 3.1 and 3.9 in Bevington. The questions are reproduced below in case you don't have the book.
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 (e.g., 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
3.9: 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 in this file.
a) Find the mean decay rate and its standard deviation. Compare the standard deviation ot 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.
Answer to 3.9 a):
From the student's data, the mean decay
rate is 3.61 decays per minute with a standard deviation of 1.87.
From the accepted mean value of 3.7 and assuming the decays per minute
will follow a Poisson distribution, the standard deviation would be 1.92.