January 6, 2014
Math 318 Assignment 1 Solutions
1. (a) E c F Gc
(b) E F Gc
(c) E F G
(d) (E F ) (E G) (F G)
(e) E F G
(f) E c F c Gc (or (E F G)c )
(g) (E F c Gc ) (E c F Gc ) (E c F c G)
(h) (E F G)c
2. As seen in class, the number of words is given by
1
March 3, 2014
Math 318 Assignment 6. Due Monday, March 10 at start of class
1. (a) Consider a simple random walk on the interval cfw_0, 1, . . . , 10 with reecting barriers
and started at 0. Find the expected number of times the walker visits position 5 b
January 20, 2017
Math 318 Assignment 3: Due Friday, January 27 at start of class
I. Problems to be handed in:
1. The following gambling game is called wheel of fortune or chuck-a-luck. A player chooses a number
from 1 to 6. Three fair dice are rolled, and
January 13, 2017
Math 318 Assignment 2: Due Friday, January 20 at start of class
I. Problems to be handed in:
1. Credit card transactions can be legitimate or fraudulent, and the proportion of fraudulent transactions is assumed to be one per thousand. Pri
Math 318/201
Probability with Physical Applications
Jan-Apr, 2017
Instructor: Dr. G. Slade, MATX 1211, 604-822-3781, [email protected]
Office hours: Mon. 16:0016:50, Wed. 13:0013:50, Fri. 10:0010:50, or by appointment.
Course website: http:/www.math.ubc.
March 13, 2015
Math 318 Assignment 8: Due Friday, March 20 at start of class
Test 2 will be held in class on Wednesday March 25, and will be based on the material covered in
Assignments 58. No assignment is due March 27. Assignment 9, which is the last on
Math 318
Solutions to Assignment #9
April 8, 2015
Total marks = [30].
1. (a) Draw the transition diagram. Not irreducible. Classes are cfw_0, cfw_1, 2, cfw_3, 4, 5. States
3,4,5 are recurrent; 0,1,2 are transient; 1,2 have period 2; 0,3,4,5 are aperiodic.
Math 318
Solutions to Assignment #8
March 20, 2015
Total marks = [30].
1. Let X be the initial number of passengers and let S be the number of stops. Then S =
N
N
i=1 Ii where Ii is as in the hint, so ES =
i=1 EIi = N EI1 , where we used symmetry
in the l
March 27, 2015
Math 318 Assignment 9: Due Wednesday, April 8 at start of class
Note: Benjamin Wallaces MLC hours on Thursday April 9 are cancelled and replaced by Tuesday
April 7, 12:303:30pm.
I. Problems to be handed in:
1. In each of (a,c,d), determine
Math 318
Solutions to Assignment #7
March 13, 2015
Total marks = [30].
1. (a) If there are X heads out of 6 then our estimate for p is X/6 and this is unbiased
because if X Bin(6, p) then EX = 6p and so E(X/6) = p. With the data we have,
5
our estimate fo
March 6, 2015
Math 318 Assignment 7: Due Friday, March 13 at start of class
I. Problems to be handed in:
1. A certain coin comes up Heads with an unknown probability p each time it is tossed. It is tossed
6 times, giving 5 Heads.
(a) Find an unbiased esti
Math 318
Solutions to Assignment #6
March 6, 2015
Total marks = [30].
1. Since the Zj are i.i.d., the moment generating function of Y is
2
2
2
MY (t) = EetY = (EetZ1 ) (EetZn ) = (EetZ1 )n .
1
For t < 2 ,
2
2
2
2
1
1
ez (12t)/2 dz
etz ez /2 dz =
2
2
1 y
Math 318
Solutions to Assignment #4
February 6, 2015
Total marks = [30].
1. (a) FX (x) = x 2 for 2 x 3 so
[1]
0
1
FT (t) = P (T t) = P ( X 2 t) = P (X 2t) =
2t 2
2
1
(t < 2)
(2 t 9/2)
(t 9/2).
(b)
0
(t < 2)
fT (t) = FT (t) = 1/ 2t (2 t 9/2)
0
(t 9/2).
[
January 6, 2017
Math 318 Assignment 1: Due Friday, January 13 at start of class
I. Problems to be handed in: Always provide clear explanations of your solutions, not merely
answers. In particular, in problems involving permutations and combinations, be su
Math 307: Problems for section 3.3
March 15, 2011
1. Show that for v, w Cn
v + w2 = v2 + w2 + 2 Re(v, w)
and use this to prove the polarization identity
v, w =
"
1!
v + w2 v w2 + iv iw2 iv + iw2
4
v + w2 = v + w, v + w
= v, v + v, w + w, v + w, w
= v2 + v
Math 307: Problems for section 3.4
November 19, 2009
1. Calculate the Fourier coecients (cn s, an s and bn s) for the triangle function
!
2t
if 0 t 1/2
f (t) =
2 2t if 1/2 t 1
and show that the Fourier series decomposition of f (t) may be written
f (t) =
Math 307: Problems for section 4.1
November 23, 2009
1. For the following matrices find
(a) all eigenvalues
(b) linearly independent eigenvectors for each eigenvalue
(c) the algebraic and geometric multiplicity for each eigenvalue
and state whether the ma