Midterm 1 Outline

Combinatorics and probability

Combinations, Ordered combinations, Permutations

How many ways

Conditional probability, multiplicative rule, independence

Discrete probability table: x, f(x)

Verify that f(x) is a probability function

Find E(X)

Find V(X)

Find E(g(X)) where g(X) is some function of X

Continuous probability density function: x, f(x)

Verify that f(x) is a probability function

Find E(X)

note: would be a simple polynomial function, or integral help provided

Discrete joint probability table: x, y, f(x, y)

Verify that f(x, y) is a probability function

Find marginals, conditionals, E(marginal), E(g(x, y))

Test for independence

Continuous joint probability table: x, y, f(x, y)

Test for independence

Algebra of expectation

E, V, COV for linear combinations of RVs

Discrete random variables

Binomial, Geometric, Negative Binomial, Poisson, Multinomial, Hypergeometric, Multivariate Hypergeometric

Identify the underlying and sampling distributions

probabilities, E(X), remember 1-p, remember to use tables, lack of memory property "Chaining"

Normal distribution

Using the standard normal to solve

Using tables backwards and forwards, x to z and z to x

Exponential distribution

p(X lt. some value), p(X gt. some value), E(X)

Use F(X) and 1-F(X), lack of memory, keep rate vs. time straight

Approximations to the Binomial

Poisson

Normal, correction for continuity

SQ 7, 8

Bonus problem: circuit diagram

FAQs

You are allowed one cheat sheet, front and back of a regular sheet of paper

I'll xerox tables and some formulas to hand out; I'll also scan these in and have them up on the web site so you know what to expect

Yes to calculators

On top of the table: exam, pencil/pen, calculator, cheat sheet, handout. Everything else under the table,

Please turn phones off and place in your bag under the table.

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