STAT401 PSE Part 2

Chapter 4A - Continuous RV

Continuous Random Variable
For any continuous RV P(X=c) is zero
Probability density function (pdf) instead of pmf
Cumulative Distribution Function (CDF) is still the same
Percentiles
Expected Values
Variance
Uniform Distribution

Chapter 4B - Normal Distribution

Normal Distribution
TI-84 for Normal($\mu, \si$)
N($\mu=0,\si=1$), N($\mu=0, \si=2$) and N($\mu=2,\si=2$)
Empirical Rule
Standard Normal Distribution
$z_\al$ Notation
Standardization of Normal
Using Normal Table
Use Standardization to find $F(x)$
Example: Tree Height
Finding percentile of N($\mu, \si^2$)
Ex: Find Percentile
Ex: Find Percentile 2
Ex: Tree Height 2
Ex: Cereal Box
Normal Approximation of Binomial

Chapter 4C - Exponential Distribution

Exponential Distribution
R code for Exponential($\la$)
CDF of exponential
Mean
Variance
Ex: Two Servers
Ex: Lifetime
Ex: Half Life of C14

Chapter 5A - Random Sample

Review of What We Have Learned So Far
Random Sample from $F(x)$
Ex: Simulating Random Sample in R - Uniform
Random Sample - Uniform
Ex: Simulating Random Sample in R - Normal
Random Sample - Normal(5,1)
If you change n: Normal
If you change n: Uniform
Ex: Java Applet

Chapter 5B - CLT and Spinning Wheel Example

Back to Sample Mean
In the Box Piture
How quickly does $\bar X$ converge to $E(X)$?
Central Limit Theorem
Ex: Spinning Wheel Game
Proportion of days (profit $\<0$)
Central Limit Theorem
Ex: Spinning Wheel with CLT

Chapter 6A - Confidence Interval for Mean

Central Limit Theorem
Three Scenarios
Confidence Interval for $\mu$
Ex: Hydro Turbines 1
One Sided CI
Ex: Hydro Turbines 2
Use of CI
What Confidence means and doesn't mean
When $\sigma$ is unkown ($n$ is still $> 40$)
Ex: A/C unit lifetime 1

Chapter 6B - When N is small