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
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).
[
Math 318
Solutions to Assignment #5
Feb. 27, 2015 (2d corrected Mar. 2)
Total marks = [30].
1. (a) N5 is Poisson(5) so its mean is 5.
[1]
(b) S3 is Gamma(3, ) so its mean is 3/.
(c) P (N5 < 3) = e
5
[1]
2
(1 + 5 + 25 /2).
[1]
(d) If you like doing integra
February 27, 2015
Math 318 Assignment 6: Due Friday, March 6 at start of class
I. Problems to be handed in:
n
2
1. Let Z1 , . . . , Zn be i.i.d. standard normal random variables, and let Y = i=1 Zi . (Y is said to
have a chi-squared distribution with n de
February 13, 2015
Math 318 Assignment 5: Due Friday, February 27 at start of class
I. Problems to be handed in:
1. Let cfw_Nt : t 0 be a Poisson process of rate , and let Sn denote the time of the nth event.
Find:
(a) E(N5 );
(b) E(S3 );
(c) P (N5 < 3);
(
January 30, 2015
Math 303 Assignment 4: Due Friday, February 6 at start of class
Reminder: Test 1 will be held in class on Wednesday February 11, and will be based on the material
covered in Assignments 14. No assignment will be given on February 6; Assig
Math 318
Solutions to Assignment #3
January 30, 2015
Total marks = [30].
1. Let X denote the players prot and Y the number of times the players number appears
on the dice. Note that X = 1 if Y = 0, and that X = k if Y = k for k = 1, 2, 3. Also,
3
1
5
Y Bi
January 16, 2015
Math 318 Assignment 2: Due Friday, January 23 at start of class
I. Problems to be handed in:
1. A test for drug use correctly diagnoses 100% of drug users and 95% of non-users. Suppose that
among the test population, 1% use the drug. Dete
January 23, 2015
Math 318 Assignment 3: Due Friday, January 25 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 9, 2015
Math 318 Assignment 1: Due Friday, January 16 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 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
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.
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
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.