MATHEMATICAL TRIPOS
Part III
Tuesday 3 June 2008
9.00 to 12.00
PAPER 37
STOCHASTIC CALCULUS AND APPLICATIONS
Attempt no more than FOUR questions.
There are SIX questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
SPECIAL REQUIREME
MATHEMATICAL TRIPOS
Part III
Friday 30 May, 2003
9:00 to 12:00
PAPER 40
Biostatistics
Attempt FOUR questions.
There are six questions in total.
The questions carry equal weight.
You may not start to read the questions
printed on the subsequent pages until
MATHEMATICAL TRIPOS
Part III
Thursday, 4 June, 2009
9:00 am to 12:00 pm
PAPER 40
TIME SERIES AND MONTE CARLO INFERENCE
Attempt no more than FOUR questions.
There are SIX questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
SPECIAL
MATHEMATICAL TRIPOS
Part III
Thursday 31 May 2001
9 to 11
PAPER 36
MAGNETOHYDRODYNAMICS
At least TWO questions should be attempted.
Complete answers are preferred to fragments.
The three questions are of equal weight.
You may not start to read the questio
MATHEMATICAL TRIPOS
Part III
Friday, 4 June, 2010
9:00 am to 11:00 am
PAPER 38
ACTUARIAL STATISTICS
Attempt no more than THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
SPECIAL REQUIREMENTS
Cov
MATHEMATICAL TRIPOS
Part III
Wednesday, 3 June, 2009
9:00 am to 12:00 pm
PAPER 38
APPLIED STATISTICS
Attempt no more than FOUR questions.
There are FIVE questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
SPECIAL REQUIREMENTS
Cov
MATHEMATICAL TRIPOS
Part III
Tuesday 3 June 2003
9 to 12
PAPER 38
APPLIED STATISTICS
Attempt FOUR questions.
There are five questions in total.
The questions carry equal weight.
You may not start to read the questions
printed on the subsequent pages until
MATHEMATICAL TRIPOS
Part III
Thursday 27 May, 2004
9:00 to 12:00
PAPER 37
Applied Statistics
Attempt FOUR questions.
There are five questions in total.
The questions carry equal weight.
You may not start to read the questions
printed on the subsequent pag
MATHEMATICAL TRIPOS
Part III
Monday 4 June 2001
1.30 to 4.30
PAPER 40
GALAXIES
Answer THREE questions. The questions are of equal weight.
Questions for which both parts are completed score more highly than two partial answers.
You may not start to read th
MATHEMATICAL TRIPOS
Part III
Friday, 4 June, 2010
PAPER 40
SUPERSYMMETRY
Attempt no more than TWO questions.
There are THREE questions in total.
The questions carry equal weight.
Please use the following conventions
[
D =
=
9:00 am to 11:00 pm
12 = 12 =
MATHEMATICAL TRIPOS
Part III
Tuesday, 1 June, 2010
9:00 am to 12:00 pm
PAPER 37
APPLIED STATISTICS
Attempt no more than FOUR questions.
There are FIVE questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
SPECIAL REQUIREMENTS
Cover
MATHEMATICAL TRIPOS
Part III
Thursday 9 June, 2005
9 to 12
PAPER 37
QUANTUM INFORMATION THEORY
Attempt FOUR questions.
There are FIVE questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet
None
Treasury tag
Script paper
MATHEMATICAL TRIPOS
Part III
Friday 3 June, 2005
9 to 12
PAPER 40
MATHEMATICS OF OPERATIONAL RESEARCH
Attempt FOUR questions.
There are SIX questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
SPECIAL REQUIREMENTS
Cover sheet
None
MATHEMATICAL TRIPOS
Part III
Thursday 30 May 2002
9 to 12
PAPER 36
APPLIED STATISTICS
Attempt FOUR questions
There are five questions in total
The questions carry equal weight
You may not start to read the questions
printed on the subsequent pages until
i
MATHEMATICAL TRIPOS
Part III
Monday 12 June, 2006
1.30 to 3.30
PAPER 36
SPREAD OF EPIDEMICS AND RUMOURS
Attempt THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
SPECIAL REQUIREMENTS
Cover sheet
1/ (a)
& & = & k t i - b - k = J J
& Vin = iR + eb = iR + k t
i =
& Vin - k t R
& V - k t & k t in - b - k R & & = J
2 & + k t / R + b + k = k t V & in J J RJ (b) H ( s) = kt / RJ (k / R) + b s2 + t s+k/J J
2
(
)
(c) i) When the derivates are set to zero
Solutions Test 1 PHYS 1004 Summer 2010 1. The Coulombs force between two protons is F = 3 108 N when the distance between them is ( in m) Fc = k (e)2 /r 2 so r = k e2 /F = 8.76 1011 . 2. A metallic sphere of radius 20 cm is charged to surface charge densi
STAT 3502 Solution-Sample Midterm Solution: 1. a) 0.27, b) 0.143, c) mean=2, standard deviation=1.41, d) 0.135, e) 0.00148 (use binomial (5,0.865) 2. q 3 p when p=P(win) 3. 0.536, 15/8 4. a) cfw_A, B, AB, No-defect, b) 7/100, c) 5/100, d) 3/100, e) 15/100
STAT 3502 Solution for assignment # 2
Total mark=25
1. Two fair six-sided dice are tossed independently. Let M = maximum of the two tosses. a. [2] What is the pmf of M ? b. [2] Determine the cdf of M and graph it. Sol:
2. [2] Let x = the outcome when a fa
STAT 3502 Solution for assignment # 1
Total mark=25
1. For hard drives to operate properly, the distance between the read/write head and the disk must remain between tight limits. From each hours production, 40 drivers are selected and the distance is mea
STAT 3502 Solution for Assignment # 4 Due: 19 July, 2010 prior to the start of class
Total mark=25
1. Suppose that a random sample of size n is drawn from the Bernoulli distribution f ( x; p ) = px (1 p)1x 0 x = 0, 1 otherwise.
Find a maximum likelihood e
STAT 3502 Assignment # 3 Total mark=25 Due: 19 July, 2010 prior to the start of class
1. If two random variables have the joint density f (x, y ) =
6 (x 5
+ y2)
0
0 < x < 1, 0 < y < 1 otherwise.
a. [1] Find the probability that 0.2 < X < 0.5 and 0.4 < Y <
STAT3502
Solution for assignment # 3
1. a. E (X ) = xi P (xi ) = 0.2 + 0.2 + 0.15 = 0.55 V (X ) = x2 p(xi ) 2 = 0.2 + 0.4 + 0.45 (0.55)2 = 0.7475 i x = 0.7475 = 0.865 b. c. Skewed to the right. Based on the CLT Shape of distribution of X is normal (bell s
Solution for assignment # 2 1. a) = 2, P (X 2) = 1 P (X 1) = 0.594
b) = 4, P (X = 0) = e4 = 0.018 c) P (X = 0|10 calls before) = P (X = 0) = 0.018, because the # of events in any interval are independent from that of any other mutually exclusive interval
Solution for assignment # 1 1. a) X = b) = 185.377 P.O.M = 0.5(31 + 1) = 16 X = 150.58 Since there is no outlier in this set of data, so mean is more appropriate than
X2
( Xi ) 2
Xi n
=
5746.7 31
median. (Upper fence is 491.56).
i n c) S 2 = = 30 n1 2= S=
STAT 3502 Sample Midterm 1. A certain type of circuit board contains 200 diodes that function independently of each other. Each diode has probability 0.01 of failing. a. What is the approximate probability that exactly two diodes will fail? b. What is the
PHYS 1004 Summer 2010 MIDTERM Solutions
Wed. July 28th
7:00 -8:30 PM
Multiple choice questions, 3 points each, answer 10 : ( circle the answer closest to the correct result) 1. Chose the dipole with highest potential energy with respect to constant extern