Monty Hall Problem:
Game show host offers you 3 choices.
2 doors behind which hide a goat; the third a car.
Suppose you choose door 1, he then opens door 3. You are given the chance to switch
your choice to door 2.
What is your choice?
The game show host problem
Game show host offers you 3 choices.
2 doors behind which hide a goat; the third a car.
Suppose you choose door 1, he then opens door 3.
You are given the chance to switch your choice to
door 2.
What is your choice?
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Chapter 4: Bivariate Distributions
STAT2001
2016 Term I
Outline
1. Two Discrete Random Variables
2. Two Continuous Random Variables
3. Independence
4. Expectation
5. Covariance and Correlation
(Textbook chapters: 4.1 - 4.4 of 9th edition or 4.1 - 4.3 of 8
Chapter 2: Discrete Distributions
STAT2001
2016 Term I
Outline
1. Discrete random variables
2. Mathematical expectation
3. Binomial distribution and Hypergeometric distribution
4. Moment generating function
5. Poisson distribution
(Textbook chapters: 2.1
STAT2001 Assignment 2
Do all 7 questions. Show your steps clearly.
Deadline for this assignment is 21st Oct. 5:00p.m. You can submit to the assignment locker (next
to LSB 125) or to your Tutors.
1. If the cumulative distribution function of X is given by
1st supplementary note for ch.1
1. Proof of the inclusion-exclusion formula (p.17):
P(C1 .Cn ) p1 p2 p3 . ( 1) n1 pn
n
Remark : p1 P (Ci ), p2
i 1
P (C
i
C j ), p3
1i j n
P (C
i
C j Cl ),.
1i j l n
Use Mathematical Induction (see remark):
A, The for
STAT2001 Assignment 3
Do all 6 questions. Show your steps clearly.
Deadline for this assignment is 9th Nov. 5:00p.m. You can submit to the assignment locker
(next to LSB 125) or to your Tutors. You can also submit electronically through Blackboard.
1. A f
Chapter 1: Fundamental Concepts
STAT2001
2016 Term I
Outline
1. Random experiments and Sample Space
2. Probability
3. Methods of enumeration (Counting)
4. Conditional probability
5. Independent events
6. Bayess theorem
Textbook chapters 1.1 - 1.5 (9th edi
Chapter 3: Continuous Distributions
STAT2001
2016 Term I
Outline
1. Continuous random variables
2. The Uniform distribution and Exponential distribution
3. The Gamma distribution and Chi-square distribution
4. The Normal distribution
(Textbook chapters: 3
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(10 Wm;
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m l0 A A1,- are everxcs ml AmAy/A rhythm
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Statistics and Probability |
Confidence Intervals
Sect. 7.1-7.2
Week 12 Given a random sample X1,X2,. .an from a normal distribution N(n,cr2),
we can find a number zap from Table V in Appendix B such that
f- M
P _zarf2 S it 2:43er 2 1 _ Of.
cfw_IA/E _
F
Statistics and Probability l
Conditional Distributions and Joint Distributions for
Continuous Random Variables
Sect. 4.3 4.5, 5.3
Week 6 4.3 CONDITIONAL DISTRIBUTIONS
Definition 4.3-I
The condinnal pmbability mass funetinn of X , given that Y = y, is defi
Statistics and Probability |
More Confidence Intervals and Sample Size
Sect. 7.37.5
Week 13 In general, when observing n Bernoulli trials with probability p of success on
each trial, we shall find a confidence interval for p based on Y/nr where Y is the
n
Statistics and Probability |
Maximum Likelihood and Linear Regression
Sect. 6.4-6.5, 6.7
Week 11 Let XLXL. . . ,X be a randem sample frem a distribution that depends en
one or mere nnknewn parameters 91,92, . . . ,9, with pmf er pdf that is denoted
by x;
Statistics and Probability |
Chisquare Distribution
Sect. 3.2-3.3, 5.4-5.5
Week 9 Let W denete the waiting time until the first eeenrrenee during the observation ef a
Peissen preeess in which the mean number cfw_If eeenrrenees in the unit interval is it.
Statistics and Probability |
Normal Distribution and Correlation for Discrete Distributions
Sect. 3.3, 4.1 4.2
Week 5 3.3 THE NORMAL DISTRIBUTION
The random variable X has a normal distribution if its pdf is defined by
f(x) = 0327? eXp|:(x2;':)2], 00 <
Statistics and Probability |
Central Limit Theorem and Chebyshev's Inequality
Sect. 5.4 5.6, 5.8
Week 7 5.4 THE MOMENT-GENERATING FUNCTION TECHNIQUE
Theorem If X1,X2, . . . ,XjFI are independent random variables with respective moment
5-4-l generating fun
4.3-4
a)
P(a y has red eyes) = P(genes = (R,R) or (R,W) or (W,R)
= (1/2)2 * 3 (one gene from each parent and equal chance to get either gene)
= 3/4
Since n = 400, X Binomial (400, 0.75)
b)
E(X) = np = 400 (0.75) = 300
Var(X) = np(1-p) = 400(0.75)(0.25) =
STA2001
Assignment 4 Solution Part 1
3.3-5
W = a + (b - a)Y, a < b
a)
F(w) = P(W w)
= P [a + (b - a)Y w]
= P [Y (w - a)/(b - a)]
(wa)/(ba)
= 0
1 dy
= (w-a)/(b-a) for a w b
b)
f(w) = F(w) = 1/(b-a)
W Uniform (a, b) where a w b
3.3-14
T exp(5), f(t) = 1/5 e
Correction to Homework3
2.5.2-(d)
not hypergeometric distribution, this distribution without
specified name.
2.5.2-(f) not hypergeometric distribution, this distribution without
specified name.
Correction to 3.2-22 of Assignment 3
Because X is in thousand
STA2001A/B Chapter 5 Exercise
Please refer to your textbook for the questions.
5.2-2,8,14,18
5.3-4,6,12,14
5.4-6,8,16
5.5-4,6,10
Solution of this exercise will be provided shortly on the tutorial page.
STA2001A/B Assignment 5
Please refer to your textbook for the questions.
4.2-8,10
4.3-4,10,14
4.4-8,14
4.5-4,6,12
4.6-10,12,20
Submit your assignment to the STA2001 assignment box besides the statistics
laboratory at or before 5pm 29th November, 2005 (Tue
STA2001A/B Assignment 4
Please refer to your textbook for the questions.
Q3.3-5, 3.3-14
Q3.4-6, 3.4-14, 3.4-16,
Q3.5-2, 3.5-6, 3.5-10,
Q4.1-8, 4.1-10, 4.1-12
Submit your assignment to the STA2001 assignment box besides the statistics
laboratory at or befo
STA 2001 Assignment 1 Solution
1.1-2 a) The outcome space = cfw_ggg, ggb, gbg, bgg, bbg, bgb, gbb, bbb
b) The outcome space = cfw_Male, Female
c) The outcome space = cfw_100-999
1.2-8 a)
P ( A B ) = P ( A) + P ( B ) P ( A B )
= 0.4 + 0.5 0.7
= 0.2
b)
P (
STA2001A/B Assignment 3
Please refer to your textbook for the questions.
Q2.5-2
Q2.6-4, 2.6-8,
Q3.2-6, 3.2-22, 3.2-24
Submit your assignment to the STA2001 assignment box besides the statistics
laboratory at or before 5pm 21st October, 2005 (Friday).
This