Chapter 1
Descriptive Statistics
1.1 What is Statistics? Statistics is the science of collecting, summarizing and analyzing data that are subject to random variation.
Data collection Data analysis experimental design survey sampling Data collection observ
Math 144: Solutions to the Final examination (Spring 2010)
*
This exam will be
2 hours long.
Please show all your work so that you do not lose any marks.
Unless otherwise specied, numerical answers should be either exact or correct to 4
decimal places.
MATH 144 Applied Statistics
Final Examination (December 2008)
Signature:
Tutorial Session:
NAME:
Student ID:
Instructions:
1. Do NOT turn over the examination paper until you are told to do so.
2. Turn o all the communication devices during the examinatio
08 Fall Math 144
Final Exam Suggested Sol
1 (a) (8 points)
y 1
0.4
(i) f y ( y ) 0.3
y0
0.3
y 1
(ii) E(Y) = 1(0.4) + 0.3 = 0.1
(iii) P(X + Y < 1) = 0.2 + 0.1 + 0.1 = 0.4
(iv) E(XY) = 1(0.1) + 0.15 2(0.1) + 2(0.05) = 0.05
(b)
(4 points)
EX = 40, X 24
P (|
Math 144: (Solutions) Final examination 2009/2010,
Dec 16, 2009.
*
All answers should be either exact or correct to 4 decimal places.
*
1. [10 marks] Poker dice is played by simultaneously rolling 5 fair dice. Find the following probabilities:
(a) Pcfw_no
Math 144: Final examination 2009/2010, Dec 16, 2009.
*
All answers should be either exact or correct to 4 decimal places.
*
1. [10 marks] Poker dice is played by simultaneously rolling 5 fair dice. Find the following probabilities:
(a) Pcfw_no two alike,
The Hong Kong University of Science & Technology
MATH244
Applied Statistics
Final Examination Spring 03/04
Answer ALL questions
Date: 22 May 2004 (Sat)
Time allowed: 2 Hours
_
PART I:
1.
Identical twins come from the same egg and hence are of the same sex
MATH 244
Applied Statistics
Final Examination
December 18, 2002
Please read the following instructions carefully before you begin the examination.
1. Do not begin until you are told to do so.
2. Please place your student identity card on your desk for ver
Chapter 10 Regression Analysis
We are often interested in comparisons among several distributions or relationships among several variables. A study of data often leads us to ask whether there is a cause-and-eect relation between two or more variables. Reg
Chapter 9 Hypothesis testing
9.1 Introduction
Condence intervals are one of the two most common types of statistical inference. Use them when our goal is to estimate a population parameter. The second common type of inference has a dierent goal: to assess
Chapter 8 Point Estimation and Condence Interval
8.1 Point estimator
The purpose of point estimation is to use a function of the sample data to estimate the unknown parameter. Denition 8.1 A parameter is a constant that describes the population. A statist
Chapter 7 Sampling Distributions
7.1 Random Sampling
Recall: population consists of the all elements we are concerned and sample is a subset of a population. Now assume that the population has a probability density function f (x). Denition 7.1 A random sa
Chapter 6 Jointly Distributed Random Variables
6.1 Joint Distribution Functions
Denition 6.1 For any two random variables X and Y , the joint cumulative distribution function ( joint c.d.f. ) of X and Y is dened by F (a, b) = P (X a, Y b) FX (a) = P (X a)
Chapter 5 Special Discrete and Continuous Distributions
5.1 The Bernoulli and Binomial distributions
Denition 5.1 An experiment is called a Bernoulli trial if the outcome can be classied as either a success or failure. In the Bernoulli trial, let p = P (s
Chapter 4 Mathematical Expectation
4.1 Expected value of a discrete random variable
Examples: (a) Given 1, 2, 3, 4, 5, 6. What is the average?
(b) Toss an unbalanced die 100 times. Lands on 1 Probab. .1 23 .3 .1 45 .2 .2 6 .1
Suppose we shall win $i if th
Chapter 3 Random Variables and Probability Distributions
3.1 Random Variables
Denition 3.1 A random variable (r.v.) is a real-valued function dened on the sample space.
There are mainly two types of random variables: discrete: taking nite or countably in
Chapter 2 Probability Probability theory is a branch of mathematics dealing with chance phenomena. The origins of the subject date back to the Italian mathematician Cardano about 1550, and French mathematicians Pascal and Fermat in 1654. The modern mathem
Pie Chart
A sample of 50 New Car Purchases Toyota 16% Ford 28%
Hyundai 16%
Honda 22%
Chevrolet 18%
1
Bar Chart
A Sample of 50 New Car Purchases 16 14 12 10 8 6 4 2 0 Chevrolet Ford Toyota Car Purchased
2
Frequency
Honda
Hyundai
Histogram
25 20
15
10
5
0 4
Math 144: Final examination (Spring 2010)
*
This exam will be
2 hours long.
Please show all your work so that you do not lose any marks.
Unless otherwise specied, numerical answers should be either exact or correct to 4 decimal
places.
*
1. (a) [5 mark