STAT234: Lecture 4 - Sums of random Variables
Sabyasachi Chatterjee
Week #5: Page 1 of 33
Binomial Distribution and Normal approx.
More generally if X1 , X2 , , Xn be independent identically
distributed (iid) Ber (p) random variables,
then
Yn =
n
X
Xi Bin
STAT234: Lecture 7 - Type I, Type II and Power
Sabyasachi Chatterjee
Week #5: Page 1 of 23
Last class
Week #5: Page 2 of 23
Last class
I
Type I error : Probability that we reject the null hypothesis
when it is true (fair for statistician)
Week #5: Page 2
STAT234: Lecture 6 - Confidence Intervals
Sabyasachi Chatterjee
Week #5: Page 1 of 31
A Romantic Experiment !
Week #5: Page 2 of 31
You and your boss !
Week #5: Page 3 of 31
I
Boss: Give me the value of p, the actual proportion of people
leaning right whi
STAT234: Lecture 5 - Hypothesis Testing
Sabyasachi Chatterjee
Week #5: Page 1 of 38
I
Random Experiment- States, Events
Week #5: Page 2 of 38
I
Random Experiment- States, Events
I
Random Variables - functions on states
Week #5: Page 2 of 38
I
Random Exper
Stats250ReviewQuestions~Tryit!
Here is a set of optional questions that demonstrate the level of math/algebra skills used in Stats 250.
Whynottrythemoutforsomereview.AswithallassignmentsinStats250,toreceivecredityoumustshow
allworkandwhereappropriate,carr
Statistics Help Card
Summary Measures
Sample Mean
x
x1 x2 . xn
n
x
n i
Sample Standard Deviation
( xi x )2
s
n 1
Normal Random Variables
standard score
observation mean x
standard deviation
If X has the N ( , ) distribution, then the random variable
Lab 2: Probability and Random Variables
Objective: The objective of this lab is to become familiar with using the models for random variables and
to find the probabilities associated with the models you have learned. The probabilities we compute
from thes
1. z-CI for m (equal probability with replacement sampling):
xz
s
n
(z = 1, 1.96, 3.09 for 68%, 95%, 99% confidence)
P(m is covered by x z
s
) ~ P( Z < z), n large.
n
2. Hybrid z-CI for m (eq-prob with replacement sampling):
Desired hybrid z-CI half width
Final exam prep 8 - 13 - 10 Try these. Not handed in. Will go over in class. Report errors.
1. z-CI for p. An equal probability with replacement sample of 100 persons is selected from
customers of a store by randomly alerting a clerk at checkout. Customer
Assignment due 7-23-10
Probability histogram, population and sample sd, etc.
1. For the following data:
2.6 6.3 6.5 2.9 6.7 6.5 5.8 2.6 8.8 4.6 5.5 4.3
incl
incl
incl
incl
a. The height of the probability histogram over the class interval [2.5, 4.5].
heig
Bonus quiz 7-21-10 8am
Probability, Random Variables, Expectation, Std Deviation ,
DO NOT REDUCE ANSWERS.
LEAVE SUMS, PRODUCTS, FRACTIONS UNEVALUATED.
l NEED TO WITNESS YOUR REASONING.
1. A box has colored balls: 1%. Successive draws are without replace
Statistics Help Card
Summary Measures
Sample Mean
x
x1 x2 . xn
n
x
n i
Sample Standard Deviation
( xi x )2
s
n 1
Normal Random Variables
standard score
observation mean x
standard deviation
If X has the N ( , ) distribution, then the random variable