Physics 1140, Fall 2001
Due 5 pm, Weds. Feb. 27
Homework Set #5
name printed:_________________________________
ID no. _____________________________
My lab section number: ________
Reminder: No Lecture 2/27 or 3/1; Review Lecture 3/7 or 3/8; Exam 3/14 or 3/15
1. Two students measure the rate of emission of alpha particles from a certain radioactive
sample. Student A watches for 2 minutes and counts 64 particles. B watches for one hour
and counts 1600 particles.
a) ( 1 point)What is the uncertainty in A's result for the number of particles emitted in 2
min?
Error in NA____________
b)( 1 point) What is the uncertainty in B's result for the number of particles emitted in one
hour?
Error in NB____________
c) (4 points) Each student now determines the rate of emission in particles per minute.
What are the two students answers for the rate, with their uncertainties? Do the separate
determinations of the rate agree?
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2. (4 pts) Principle of Maximum Likehood, Paraphrase of Taylor Problem 5.26:
Suppose we have N measurements x1, x2, ….xN of the same quantity x, and we believe
that their limiting distribution should be the Gaussian function GX,  (x), with X and 
unknown. Differentiate the natural logarithm of "Prob (..)=…" in Taylor Eq. 5.40 with
respect to , and show that the maximum occurs when  is given by Eq. 5.43.
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