Discrete Calculus & Probability
MCS 256: Discrete Calculus & Probability
Unit 4 Outline
-
Special discrete probability distributions
-
Discrete probability distributions and
their related summation formulas
- Binomial theorem
- Geometric series
- (Newton's) binomial series
- Vandermonde identity
- Exponential series
-
- Joint distributions of discrete random variables
- Joint probability function
- Marginal probability functions
- Conditional probability functions
- Independent random variables
-
Mean/expected value
- Techniques for calculating expected values
- Look 'em up
- Summation calculus
- Probabilistic insight
- Generating functions
- Mean/expected value of a discrete random variable
or distribution
- Law of the Unconscious Statistician
- Probability generating function
- Moments
- Ordinary moments, central moments,
factorial moments, variance, standard deviation
- Covariance, correlation (coefficient)
- Moment generating function:
not on the exam
- Means, covariances, and variances of sums
of r.v.s or linear combinations of r.v.s
- Proofs that really count
- Proving Fibonacci identities by counting
- Generating functions
- (Ordinary) generating functions
- Probability generating functions
- Exponential generating functions
- Moment generating functions