Exercise 5.1 - Nuclear Decays
In this exercise we shall simulate the measurement of
the number of radioactive decays measured in one second
from a particular radioactive source. You will choose the number of
times to repeat the measurement, and the estimated mean and
the estimated standard deviation will be calculated and a
histogram of the data will be displayed.
When through with this exercise
you should answer the following questions:
-
Does the width of the "curve" as measured by the
estimated standard deviation depend on the number
of times the measurement is repeated?
-
The simulated events were generated by a Monte
Carlo technique, named after the casino.
This algorithm does an excellent job of simulating
what real data would look like.
The true mean and standard deviation used in
the Monte Carlo calculation are integers.
What are their values?
-
For a given number of repeated measurements, the
values of the estimated standard deviation were
unlikely to ever come out exactly equal to your
answer to Question 2, but instead for a number
of trials exhibit a spread of values.
Qualitatively, how does the width of this spread of
values depend on the number of repeated measurements?
-
Can you find any relationship between the two
numbers that were your answer to Question 2 above?
A correct answer to this question matches the relationship
between the mean and standard deviation for real
radioactive decays.
-
As of January 18, 2001 hockey player Mats Sundin of
the Toronto Maple Leafs had scored 16 goals in the
season. Some were "lucky" goals and at other times
he had excellent scoring chances that failed to find
the net.
From your answer to Question 4, what is a reasonable
guess of the statistical uncertainty in the number
of goals he has scored.
This document and the Perl code to generate the simulation were written by David M. Harrison, January 2001.
This is $Revision: 1.6 $, $Date: 2001/05/31 14:45:11 $ (year/month/day) UTC.