Lecture 6: Discrete Random Variables (DRV)
Discrete Random Variables (DRVs): variables that can only assume a finite set of precisely
countable values
Example: scores on a test where each item is scored 0 or 1
Possible scores: 48 63
78
94
Impossible score
Lecture 7: Using Binomial Experiments to Test Hypotheses
Null hypotheses and alternative hypotheses
Rejection regions and decision rules
Type I and Type II errors
and
Coin tossing
task: experiment try to figure out, is the
coin fair or biased?
Use n
Lecture 8Continuous Random Variables
Normal distribution
Z scores and p values
Normal approximation to the binomial distribution
Continuous random variables can assume an infinite number of possible values.

discrete binomial can be
calculated by co
Lecture 9: Sampling Distribution
Hypothesis testing
the sampling distribution of the mean is the distribution of the means of all possible samples of
a given size that could be drawn from a population
How many such samples might there be?
Even with a sm
Lecture 11: Simple sample t Test about
Review
1. Generic, 2 2 tailed, 34 1 tailed
Large sample (n >30)?
Small sample (n<30)?
Do we know the SD?
we only know the sample sd
Sx is sd
t critical defined by degrees of freedom
(n1) degree of freedom
Examples
Lecture 10: LargeSample Hypothesis Testing about
Review of concept
Logic behind the rule,
X number of outcomes
Why does it work?
probability is really small
If the coin is fair. If the coin is biased then well get more 910 heads,
If its fair then its r
May 6th lecture
Statistical Terminology
. Statistics: involves the measurement, description, and analysis of variables
. Variables: anything that can be measured and which show some variability in the population (eg.
Height, weight, scores on test (nume
Lecture 3:
Interpreting Standard Deviation
From last lecture
more than 10 times larger
 Since they had the same variable, we can just compare the 2 standard deviation and there is
substantial more variability in sample 2 than 1.
Suppose we have just on
Lecture 4:
Probability
Random sample: a sample selected from a population such that all members of the population
have an equal probability of being selected (true random sample)
Eg
names on a piece of paper: pull out of a hat, one by one until select 4
Lecture 5: Counting rules, Compressed
Complex experiments use counting rules.
Permutations
Partitions
Combinations
Hypergeometric formula
1. Permutations: the number of different ways a set of N things can be arranged
N!( n factorial)
until (2)(1) bil