UNSW Astrophysics Postgraduate Course
Module 3, Session 2
Optical and Infrared Techniques
Lecture 5: Data Reduction and Analysis
Tutorial Questions
http://www.phys.unsw.edu.au/ 
spd/pgc_astro/part3.html
1. In a certain astrophysics postgraduate course 7.3% of students failed and 92.7% passed, averaged over many semesters.
(a) What is the expected number of failures in a particular class of 32 students, drawn from the same population?
(b) What is the probability that five or more students will fail?
2. Members of a large collaboration that operates a giant proton-decay detector in a salt mine in Queensland detected a burst of 8 neutrinos coincident with the optical detection of SN1987A.
(a) If the average number of neutrinos detected in their apparatus is 2 per day, what is the probability of a fluctuation of 8 or more in one day?
(b) In fact the 8 neutrinos were all detected within a 10 minute period. What is the probability of detecting a fluctuation of 8 or more neutrinos in this period?
3. In a scattering experiment to measure the polarization of
elementary particles, a total of N=1000 particles were scattered from
a target. Of these, 670 were observed to be scattered to the right and
330 to the left. Assume there is no uncertainty in 
.
(a) Based on the experimental estimate of the probability, what is the
uncertainty in 
and in 
?
(b) The asymmetry parameter is defined as 
. Calculate the experimental asymmetry and its uncertainty.
(c) Assume that the asymmetry has been predicted to be A=0.400. Recalculate the uncertainties in (a) and (b) using the predicted probability.
4. The observed frequency as a result of the Doppler shift when a
sound source of frequency 
is moving with velocity v towards a
fixed observer is given by 
where u is the
velocity of sound. Find the uncertainty in 
resulting from measuring uncertainties in u, v and . Assume
these values are 
m/s, 
m/s and
Hz.
5. Find by numerical integration the probability of observing a value
drawn from the Gaussian distribution that is more than (a) 
, (b)
and (c) 
from the mean.
6. The following grades were given for the astrophysics postgraduate course in 1997:
Plot a histogram of these course grades. Plot a Gaussian curve based
on the mean and standard deviation of the data, appropriately
normalised. Apply the 
test and check the associated
probability from tables. Which student are you?