Ch. 5 Stats Vocab

random process

generates outcomes that are determined by chance

• unpredictable in the short run

• eventually has a regular and predictable pattern in the long run

probability

a number between 0 and 1 that describes the proportion of times the outcome would occur in a very long series of repetitons

• express as decimal, fraction, or percentage.

empirical probability

likelihood of an event occurring based on actual experiments or observations

• use approximates for real trial

theoretial probability

calculated likelihood of an event occurring, based on the mathematical model rather than experimental data

• P(E) = (# of ways an event can occur)/(total possible outcome)

law of large numbers

as the number of trials increases, the relative frequency approaches theoretical probability

basic rules of probability

1. if all outcomes in sample space are equally likely, the probability that event A occurs is P(A) = (# of outcomes in event A)/(total # outcomes in sample space

2. probability of any even is a number between 0 and 1

3. all possible outcomes together must have probabilities that add up to 1

4. the probability that an event does not occur is 1 minus probabillity of the event occuring

complement rule

probability that an event will NOT occur

• 1 minus the probability of the event is the complement

• P(A^c) = 1 - P(A)

law of averages

a common misconception of past outcomes of a random event being able to influence future results

• “balancing out”

• misguided belief

sample space

list of all possible outcomes

simulation

imitation of chance behavior, based on a model that accurately reflects the situation

• assign numbers

• determine what you are counting and record

probability model

description of some chance process that MUST consist of two parts

1. sample space

2. probability for each outcome

event

any collection of outcomes from some chance process

mutually exclusive (disjoint)

two events that have no common outcomes, can never occur together

• P(A and B) = 0

• NEVER independent

visual images for summarizing sample space

can make either two-way table or venn diagram

• make sure to properly isolate each response in the proper section

P(A U B)

union; probability that either event A, event B, or both events occur

• P(A) + P(B) - P(A ∩ B)

conditional probability

probability that one event occurs given that another event is known to happen

• P(A|B)

calculating conditional probability

P(A|B) = P(A ∩ B) ÷ P(B)

independent events

if knowing whether or not one event has occurred does not impact the probability that the other event will happen

• yes: P(A) = P(A|B)

• no: P(A) ≠ P(A|B)

• must be exact same value

multiplication rule

P(A ∩ B) = P(A) × P(B)

• specifically only for independent events

tree diagram

shows the sample space of a chance process involving multiple stages

• Every probability after the first stage is conditional

general formula for showing independence

P(A) ≠ P(A|B)

Therefore, the events “A” and “B” are not independent. Knowing that “B” happened increases/decreases the probability of “A.”

• increases —> value is greater than 50%

• decreases —> value is less than 50%

general formula for discussing simulation results

On average, according to my simulation, ____.

• must include units if available

• include the real mean, even if in parentheses