Week 10
Central Limit Theorem
Point Estimation
Lindeberg-Levy Central Limit Theorem
(CLT)
Suppose that X 1 , X 2 ,. are iid rvs with finite mean , finite variance 2 and a mgf.
1n
X
Let X n X i and U n n
.
n i 1
/ n
Then U n d N(0,1) .
Steps to Prove the C
Week 9
F Distribution
Inequalities
Convergence
F distribution and F statistic
Chebyshevs Inequality
Applications: Used to prove many probabilistic results
including the weak law of large numbers.
Let k > 0 and let Y be a rv with mean and variance 2 .
1
1
Week 8
Finding Distribution Functions of Functions of R.V.s
Mixture and Mixed Distributions
Normal Distribution Theory
Recap Functions of R.V.s
Statisticians statistics of interest such as
sample mean and variance
Finance portfolio construction, derivativ
Week 7
Discrete Multivariate Distributions
Independence
Covariance & Correlation
Conditional Expectations
Law of Iterated Expectation
Discrete Multivariate Distributions
Example 1
A die is rolled. Let X = no. of 6s and Y = no. of even numbers.
Find the jo
Stat 2001 / Stat 6039
Week 6
Cumulative Distribution Functions
Continuous Probability Distributions
Last Week
Discrete RVs: Binomial, Bernoulli, Poisson, Geometric,
Hypergeometric, Negative Binomial
Poisson Approximation: Roll 2 dice 12 times. Find the
pr
Stat 2001 / Stat 6039
Week 5
Discrete Probability Distributions
Mathematical Expectation
Guess which distribution this data
comes from
What about these histograms?
Feeling normal?
or skewed?
How long should you wait?
Twins
Poisson introduced this distribu
1000 means of n Normal(1,1) variates (first 20 shown). Bottom cell shows
P( X n > 0.01) based on the 1000 simulations
Normal
n=5
1.5215617
0.8424143
0.3508155
0.8901758
1.1160046
0.9364359
0.9780781
0.5139878
0.4357637
1.3285609
1.6373613
1.9425456
0.8424
Stat 2001 / Stat 6039
Week 4
What is the chance of a false positive?
STAMP OUT CHLAMYDIA
1 in 14 young people in Canberra have chlamydia, but
most dont know it, because usually there are no
symptoms.
The SOC (Stamp Out Chlamydia) Project invites you to
ge
Stat 2001 Week 3
Recap Bayes Theorem
Suppose it is Wednesday night and I am at a party. I have told you that you will have a
quiz on Thursday unless I drink too much and forget. So you call my friend and ask her
Do you think Priya has drunk too much tonig
Introduction to Mathematical Statistics
Week 2
Recap
Axiom 3
Axiom 3
Recap
Whats the pr of getting 2 heads on 3 tosses of a coin?
1) What is done and what is observed?
2) Write out the sample space
3) Define a reasonable probability function
4)Express the
What is Mathematical Statistics
&
Probability ?
Descriptive Statistics
Mathematical Statistics
Stat 1008 equipped you with a set of descriptive tools which helped you
understand a restricted class of data structures. In a sense these tools were
presented
Welcome to Stat 2001 / Stat 6039
Introductory Probability
&
Mathematical Statistics
Lecturer: Priya Dev
Tutors: Mo Yang, Yeong Heng Pua
Study Essentials
Read lecture notes
Read prescribed or additional texts
Work through problems consistently
Attend lectu