1. Probability and Statistics Review
Purpose:
Review basics of probability and statistics
Define some terminology
Revisit some important distributions
Discuss how to analyze and characterize different probability distributions
Discuss applicability to performance evaluation (and CPSC )

2. Some Terminology (1 of 2) Experiment (e.g., coin flipping)
Sample space (e.g., S ={Heads, Tails})
Could be discrete or continuous
Outcome (e.g., Heads)
Event: successful outcome occurs
Randomness: unpredictable outcomes
Independence: unaffected outcomes

3. Some Terminology (2 of 2) Random variable X Probability distributions
Could be discrete or continuous
Probability density function (pdf)
f(x) = P(X = x)
Cumulative Distribution Function (CDF)
F(x) = P(X < x)
CDF is integral of pdf (continuous case)

4. Axioms of Probability Probabilities are non-negative
For any event A in the sample space S, P(A) > 0
Probabilities are normalized
P(S) = 1
Mutually exclusive events
If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

5. Describing Distributions (1 of 2)
There are several ways to summarize the key properties of a distribution:
Central tendency: mean, median, mode
Variability: variance, standard deviation, coefficient of variation (CoV), squared CoV
Moments: 1st moment, 2nd moment, …
Central moments: 1st central moment, …
Modality, index of dispersion, skewness, kurtosis, variance coefficient, …

6. Describing Distributions (2 of 2)
The most common summary statistics are the mean and the variance:
Mean: expected value (expectation)
Variance: mean squared deviation from mean
Mean is equal to the first moment
Variance can be calculated from the first moment and the second moment
Variance is equal to 2nd central moment

7. Some Common Distributions
Uniform Distribution
Binomial Distribution
Geometric Distribution
Poisson Distribution
Exponential Distribution
Erlang Distribution
Gaussian (Normal) Distribution