University of Western Ontario
Departments of Applied Mathematics
Statistics 2503B Final Examination
(Take-Home)
Code 111
April 22, 2020 24 hours
Student’s Name: Student Number:
Instructions
1. Print your Name, Student Number in the box above.
2. The Exam Booklet should have 20 pages (including the front page).
3. In Part A (Multiple Choice questions), circle the correct answer
for each multiple choice question.
4. Part B must be answered in the space provided in the Exam Booklet.
Unjustified answers will receive little or no credit.
5. Pages 18, 19 and 20 of the Exam Booklet are blank and are to be
used for Part B if you need extra space for presenting your answers
for Part B. Indicate clearly which questions from Part B you are
answering there.
6. Code of Conduct: Students are not allowed to assist or commu-
nicate to each other during the exam time. This will constitute a
scholastic offence subject to severe academic penalties. If there is any
indication of violation detected, it will result a ZERO to the exam.
7. Total Marks = Part A (30) + Part B (90) = 120 marks.
Stats 2503B Final Exam Take Home v111 2020
Part A: 15 multiple choice questions (2 marks each) = 30 marks
Do your working in the Scratch Papers. Circle the correct
answer for each multiple choice question.
A1: Adam has $1,000 in the bank right now, in an account which pays 5 %
interest (compounded continuously). At what (continuous) rate, rounded
to the nearest dollar, does Adam need to deposit money into the account
in order to have $20,000 after 20 years
A) $582 per year B) $503 per year
C) $318 per year D) $101 per year
E) none of the above
A2: The Wronskian of y1 = e 2t cos t and y2 = e 2t sin t is
A) e2t(sin t+ cos t) B) e4t
C) e 4t D) e 2t(cos t+ sin t)
E) none of the above
A3: The general solution to the differential equation y′′ 4y′ + 5y = 0 is
A) c1e2x cosx+ c2e2x sinx B) c1 sin 2x+ c2 cos 2x
C) c1ex cos 2x+ c2ex sin 2x D) c1 cosx+ c2 sinx
E) none of the above
A4: The inverse Laplace transform of F (s) = s
s2 4s+ 5 is
A) 2e2t cos t+ e2t sin t B) e2t(3 cos t 5 sin t)
C) e2t(cos t+ 2 sin t) D) e2t cos 2t+ 5e2t
E) none of the above
A5: The inverse Laplace transform of F (s) = ln
(
s 2
s+ 2
)
is
A) t
2
(t2 + 1)4
B) e
2t e2t
t
C) t 4e2t D) e
2t + e 2t
t
E) none of the above
2
Stats 2503B Final Exam Take Home v111 2020
A6: The solution to the difference equation 3y(n+ 1) = 2y(n) + 1, y(0) = 3 is
A) 2
n+1
3n
+ 1 B) 3n + 2
C) 2(2n 1 + 1) D) 3(3
n + 1)
2n+1
E) none of the above
A7: A Markov chain has a state space S = {1, 2} and transition probability ma-
trix P . In the long run, the chain spends twice as much time in state 1 as it
does in state 2. When n is large, we would expect P n to be approximately
equal to
A)
1/3 2/3
1/3 2/3
B)
2/3 2/3
1/3 2/3
