Exam 1 Review
Keegan Korthauer
Department of Sta8s8cs
UW Madison
Exam 1
1. Friday, February 28 9:55am-10:45am (50 min) in
Social Sciences 5208 (regular lecture room)
2. Counts for 25% of your nal grade
3. Bring your
Ch. 5 Joint Probability Distributions
and Random Samples
5. 1 Jointly Distributed Random Variables
In chapters 3 and 4, we learned about probability distributions for a single random variable.
However, it is often useful to have more than one random varia
Ch. 4 Continuous Random Variables
and Probability Distributions
4.1 Probability Density Functions
A continuous random variable is a random variable with an interval of real numbers for its range.
Probability Distributions for Continuous Variables
The prob
Ch. 3 Discrete Random Variables and
Probability Distributions
3.1 Random Variables
1. Random Variable A function that assigns a real number to each outcome in the sample space
of a random experiment. Notation is used to distinguish between a random variab
Ch. 2 Probability
Probability permits us to make the inferential jump from sample to population and gives us a
measure of reliability for the inference.
Example 1
Assume a die is balanced. Roll the die 10 times. Observe a 2 ten times. The probability of t
Formula sheet 2
Sample statistics
Sample size:
Sample mean:
x
=
n
(
n 2z1/2
xi
Sample variance:
T.S. =
)
1
1 ( 2
(xi x
)2 =
xi n
x2
n1
n1
Mean:
where n
:= n + 4, and p := (x + 2)/
n
E(aX + b) = aE(X) + b
Test statistic:
Variance:
V (aX + b) = a2 V (X)
Formula sheet 3
Sample statistics
Sample mean:
x
=
SST =
n
SSE =
xi
i=1
n
(yi yi )2
i=1
i=1
n
SSR =
(
yi y)2
Sample variance:
s2x =
n
(yi y)2
)
1
1 ( 2
(xi x
)2 =
xi n
x2
n1
n1
i=1
Mean Squares:
Linear transformations
MS = SS/df
Mean:
Conditional varian
Ch. 12 Simple Linear Regression and
Correlation
12.1 The Simple Linear Regression Model
Suppose we want to predict the rainfall at a given location on a given day. We could select a
single random sample of daily rainfalls, use the methods of Ch. 7 to esti