STAT 433/833 PROBLEM SET 1
1. Let cfw_Xn n=0,1,. be a Markov chain on state space
0 1/3 2/3
cfw_0, 1, 2, 3, 4 with transition matrix
1/4 3/4 .
(a) Is this chain irreducible? Is it aperiodic?
(b) Find the
Shanghai Jiao Tong University
Department of Mathematics
Stochastic Processes (Mid-term Examination)
Date: November 14th, 2013
(1)This is a closed book/note examination. Approved calculators are permitted.
(2)There are 8 questions i
STAT 833 FINAL ASSIGNMENT
FOR STAT 833 ONLY. DUE ON MONDAY, DECEMBER 8, 2014 (6PM)
1. A DTMC is called strongly irreducible, if for some n 1,
Pijn > 0,
for all i, j S.
(a) If a DTMC is strongly irreducible, then it is clearly irreducible. Give an example
Due: Wednesday, April 9, drop off at MC6148
1. Let (X1 , X2 , . . . , Xn ) be a random sample from N (, 2 ). Find the generalized likelihood ratio test of
H0 : 2 = 02
H1 : 2 6= 02 for each of the following two cases:
(a) = 0 i
STAT 450/850 Estimation and Hypothesis Testing
(Practice problems for Test 1, Friday January 30, 2015)
1. Let X and Y be independent Geometric random variables, i.e., P (X = k) = P (Y = k) = (1 p)pk ,
k = 0, 1, . Let U = mincfw_X, Y , V = max
STUDENT ID # 205 420 63
The bid that a competitor makes on a real estate property is estimated to be somewhere
between 0 and 3 million dollars. Specifically, the bit X is viewed to be a continuous random
variable with density fun
STAT 334 - Fall 2015 - Assignment 2
Due Friday Oct 30 at start of class. This assignment may be completed in pairs as before.
1. A mouse is in the centre of the maze with three choices. Door 1 leads back to the centre
after 2 minutes. Door 2 leads back to
STAT 334 Fall 2015 Tutorial 2
Names: 90 LUTlO (\l S
1. Game 1: On each turn, you roll a fair 6~sided die. You collect the puzzle piece matching
the number you rolled= if it has not been collected yet.
a. What is the expected number of turns it takes
STAT 334 - Probability Models for Business and Accounting
M3 3144 x36721
dkchisho office hours: 4-5:30 M, 1:30-3 F in M3 3106
Textbook/Course Notes: The primary source will be the notes given in class.
STAT 334 - Fall 2015 - Assignment 1
Due Friday Oct 16 at start of class
This assignment may be completed in pairs. Only one person should submit the paper. Both
names and ID numbers should be on it. Both will receive the same grade.
1. Let X be a negative
University of Waterloo
STAT 334 Test 1
First (Given) Name:
Last (Family) Name:
Student ID #:
1. Please read questions carefully and show y
STAT 334 Fall 2015 Tutorial 4
1. This will give you some practice with the Multinornial Distribution.
Roll the (biased) die 10 times and write the numbers you get in the boxes below:
3 5 2
How many 1’s: How many 2’s: How many 3’s:
biased, c119. _
STAT 334 Fall 2015 Tutorial 5
Names: 50 LUTl 0 S
This tut will give you some practice with joint transfonnations and conditioning, step by step.
1. Step 1: Find (graph) the support of U and V, for the joint transformation of X and Y
a. O<x<y<2; U = Y
STAT 334 Fall 2015 Tutorial 3
Names: SDI/UT 1 ‘ON 5
1. You throw a dalt at a board, and call the x-coordinate X. Your score is Y = “(X—7702,
where m is the X—coordinate of the middle of the board. Find the pdf and range of Y if.
a. you throw the dart
Due: Wed. Oct. 28
1. Quantile functions. Suppose a continuous random variate X has a strictly increasing cumulative distribution
function FX (x), a continuous density fX (x), and a quantile function QX
STAT 337 ASSIGNMENT 1
Due: 1:00pm October 8, 2015
Notes for Submission: Assignments are due at the start of class. Typed solutions are preferred.
1. [10 marks] In this question we will examine the incidence and prevalence of HIV/AIDS in
Canada. Some of th
STAT 337 ASSIGNMENT 1 Solution Key
1. [10 marks]
(a) [2 marks] To estimate the overall, male and female incidence rates of HIV/AIDS in
Canada in 2011 we use the formula:
Number new cases in all of 2011
July 1, 2011 populat
Exploratory Data Analysis (or Searching for Stationarity)
When an observed time series appears stationary, we can
calculate its sample autocorrelations, and use them to decide
on a model.
Many time series do not appear stationary; e.g., Johnson and
R version 3.0.0 (2013-04-03) - "Masked Marvel"
Copyright (C) 2013 The R Foundation for Statistical Computing
Platform: x86_64-apple-darwin10.8.0 (64-bit)
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under c
Lecture 2: Descriptive Statistics and Exploratory Data Analysis
Further Thoughts on Experimental Design
16 Individuals (8 each from two populations) with replicates
Pop 2 Randomly sample 4 individuals from each pop Tissue culture and RNA extraction