1. Basic Probability and Stats Review
Random variables
Discrete probability distributions
Expected value of a discrete random variable
Continuous Distributions
Working with distributions in Excel

2. Random variables (RV) and probability distributions
RV is a variable whose value depends on the outcome of an uncertain event(s)
Low bid by competing firms, project completion date
Demand for some product or service next year
# of patients requiring open heart surgery next month at Hospital H
Cost of Drug X in December, 2004
Probability of various outcomes determined by probability distribution associated with the RV
Probability distributions are the “shapes of RV’s”
As modelers, we select appropriate distributions
Probability distributions
mathematical functions
Assign numeric probabilities to uncertain events modeled by the distribution
See “Distributions, Simulation and Excel Functions” handout that Prof. Doane created and that I’ve posted on Web.

3. Two Types of Variables Discrete Distributions Integer, countable X
example: # of warranty claims in a day
P(X) is the probability at each point
P(X) may be summed over X values
Continuous Distributions
X defined over an interval
example: Length of stay for open heart surgery patients
Points have no area
Calculus gives area under curve

4. Discrete RVs and Probability Distributions
DistributionReview.xls
Countable # of outcome values
Each possible outcome has an associated probability
Expected Value of Discrete RV
A few discrete distributions
Empirical
Binomial – BINOMDIST()
Poisson – POISSON()
Expected Demand
Total Probability

5. Continuous RVs and Probability Distributions
Infinite # of outcome values
Has a probability distribution function (pdf), f(x), which you can loosely think of as P[X=b].
We calculate probabilities over intervals using the cumulative distribution function (cdf), F(x), which is P[X<=b]
Area under the f(x) curve from –infinity to b
Uniform f(x)
Exponential f(x)
Normal f(x)

6. P.D.F. vs. Cumulative Probability Density Function
X axis shows values of X
Y axis shows probability
S P(X) = 1 if discrete
 f(x) = 1 if continuous
Histogram is pdf for data
Cumulative Distribution Function
Y axis shows cumulative probability
0  F(X)  1 and is non-decreasing

7. RiskView Excel Add-In, Part of Palisade Decision Tools Suite
“Live” distribution viewing, Huge number of distributions
Online Help has background info on distributions
Start | Palisade Decision Tools | RiskView 4.5
Can also launch from within Excel from the Palisade Decision Tools toolbar (which is visible if any of the Palisade tools are running,
Have all create a Uniform(01,1). Interpret table and sliders
Change to Normal(0,1), Interpret tables and sliders

8. A few useful distributions

9. The Normal Distribution
Two parameters: Mean, standard deviation
Symmetric
Standard normal distribution has mean=0, std dev=1
Normally distributed data with any mean and standard deviation can be converted to a N(0,1) by standardizing
X~N(m,s)
Z~N(0,1)
Excel has a number of functions related to the normal distribution: NORMDIST(), NORMINV()
NORMSDIST(), NORMSINV()
Let’s review handout “Excel Functions for Working with Normal Distributions” and do the Continuous tab in DistributionReview.xls

10. Distribution Review Download DistributionReview.xls
Let’s answer questions on sheet Discrete
We’ll do Continuous sheet momentarily
Excel has many probability and statistical related functions
Remember, probability distributions are a type of model for some uncertain quantity
Think of histograms as empirical probability distribution functions

11. Descriptive Statistics in Excel
Data Analysis Tool-Pak
AVERAGE(), STDEV(), MEDIAN()
FREQUENCY()
PERCENTILE()
RANK(), PERCENTRANK()
MIN(), MAX()
2 ways to create histograms
Data Analysis Tool-Pak
Default bins
User specified bins
FREQUENCY() array function
StatReview.xls