Unit 4: Probability Basics

Probability

Probability

long run of relative frequencies; between 0 & 1;

• short term—>unpredictable

• long term—>predictable

Law of Large Numbers

If we do something many many times, the results will start to match the expected probability more closely

Simulation

imitation of chance behavior based on a model that accurately reflects the situation (dice, flip a coin, applets, random # generator)

Simulation process

1. Describe how you simulate 1 trial (one repetition)

2. Perform many trials

3. Use the results to answer the question

Mutually exclusive

can’t occur together

complement

probability of an event not happening (A^c)

Random Process

all possible outcomes that can occur are known, but individual outcomes are unknown; generates results that are determined by chance

Outcome

result of a trial of a random process

Event

collection of outcomes

Sample Space

collection of all possible non-overlapping outcomes

Adding/substracting a constant c

shape: same; center: ± by c (mean & median); variability: same (if there is an equation that says to add or subtract to find the sd, don’t do it)

Multiplying/Dividing a constant c

shape: same; center: multiple/divide by c (mean and median); variability: multiply/divide by c

BINS

binary: each trial is a success or failure; independent: each trial is independent of each other; number of trials: fixed; same probability of success for each trial

Interpreting Mean

after many many trials, the average # of success context is mean out of n

Interpreting SD

the number of success context typically varies by SD from the mean of ___ out of n

10% condition

When taking a random sample (w/o replcement) of size n from a population of size N we can use a binomial distribution if n<1/10N

Large Counts Condition

allows us to use normal distribution to model a normal distribution if np>=10 and n(1-p)>=10

Geometric: BITS

binary: each trial is a success or failure; independent: each trial is independent of each other; trials until first success occurs (not fixed); same probability of success for each trial

Describing Geometric Distributions

shape: always skewed to the right

random variable

a random process whose outcomes are numerical values

discrete random variable (x)

takes a fixed number of values with gaps between values