M I 6, ’L{'-‘—( 2) A we“ a - ,
{Mth 0509;- (52‘
950‘“ m to 19ri or!
g '3‘
(é)
dam-lore, (770‘: 2; «34$ #4 Mad Raft-M
Ltk uaﬂﬂu
44" <35 ‘9 ‘-e.
v (1"
v : ‘7 9M 0444 a. \.
(In SPEJA-Ewbr 4/1 4- (.
’28- {‘95- ExckmCApt/i < (
r. nué BL, &w}qt(er
M3 ﬂ“)
1’1:
Math 4320
Quiz # 1
Last Name:
ID #:
Problem 1
Consider Markov chain with the transition probability matrix
P =
0.2 0.3 0.5
0.1 0.7 0.2
0.3 0.3 0.4
and deterministic initial condition X0 = 1.
Compute the probability P rcfw_X2 = 2?
Using the law of total pr
Last Name:
ID # :
First Name:
Math 4320
Midterm Exam
Total = 100 points + Bonus Problem
Problem 1 (25 Points)
On each point in tennis, a player is allowed two serves. The player gets his rst serve in, about 50%
of the time. When the player gets the rst se
Math 4320
Quiz # 2
Problem 1
Consider i.i.d random variables k with probability mass function
P rcfw_k = 3 = 0.3, P rcfw_k = 2 = 0.2, P rcfw_k = 1 = 0.5.
Set X0 = 3. Consider Markov chain dened as Xn = mincfw_1 , . . . , n .
Determine the transition proba
Math 4320
Quiz # 3
Last Name:
ID #:
Problem 1
Given states (0,1,2) and the transition probability matrix
P =
0.5 0.5 0
0.5 0 0.5
0 0 1
determine the mean time to absorption from state 0.
Solution: Dene i = E[T |X0 = i], where T is the time to absorption.
Last Name: ID # : Math 4320 Midterm Exam
First Name:
Total = 100 points + Bonus Problem
Problem 1 (20 Points)
On each point in tennis, a player is allowed two serves. Suppose while playing tennis, the player gets her first serve in, about 50% of the time.
CD
"£—
3_ 0 t 2 3 4 s—
! 0 El: ‘11
i l ‘IL 0 i 2.
Z '1 0 l2-
—L——§_ {2. 0 l];—
!_ 9 i1 0 t z F
S’- kz {(1
I. mix—07W W M 7;
if
I'. _ ,
~M¥Lﬁom at), m I; '69) OL’I' AIADH ‘_
‘_——L"_T—T.““ l
Math 4320 Assignment 3
September 9, 2016
Exercise 1.5.2: A jar has four chips colored red, green, blue, and yellow.
A person draws a chip, observes its color, and returns it. Chips are now drawn
repeatedly, without replacement, until the first chip drawn
Assignment 2: Math 4320 Fall 2016
Professor William Ott
(1) (Exercise 1.3.2) A fraction p = 0.05 of the items coming off a production process are defective. If
a random sample of 10 items is taken from the output of the process, what is the probability th
Problem 1
The joint density of X and Y is given by
f (x, y) =
ey
,
y
0 < x < y,
0<y<
Compute (i) marginal probability density fY (y), (ii) conditional density fX|Y =y (x).
Hint: it is easier to compute FY (y) = P rcfw_Y y and dierentiate. Consider the joi
Produced with a Trial Version of PDF Annotator - www.PDFAnnotator.com
Intro to Stochastic Modelling
Math 4320 Quiz 8
Q1. Let N = Nt ; t 0 be a Poisson process with rate = 15. Compute:
(a) P (N6 = 9)
(b) P (N6 = 9, N20 = 13, N56 = 27)
(c) P (N20 = 13|N6 =
Last Name:
ID # :
First Name:
Math 4320
Midterm Exam
Total = 100 points + Bonus Problem
Problem 1 (20 Points)
On each point in tennis, a player is allowed two serves. Suppose while playing tennis, the player
gets her rst serve in, about 50% of the time. W
Assignment 1: Math 4320 Fall 2016
Professor William Ott
(1) (Exercise 1.2.3)
(a) Plot the distribution function
0,
F (x) = x3 ,
1,
for x 6 0;
for 0 < x < 1;
for x > 1.
(b) Determine the corresponding density function f (x) in the three regions (1) x 6 0,