1

A.P. STATS – UNIT 2 VOCABULARY

Chapters 6-8

2

(1) PROBABILITY – THE LONG-TERM, RELATIVE FREQUENCY OF AN EVENT HAPPENING.

* ANY PROBABILITY MUST BE A VALUE BETWEEN 0 AND 1, INCLUSIVE.

* IT CAN BE WRITTEN AS A DECIMAL, A FRACTION, OR A PERCENT.

UNIT 2 VOCABULARY – Chap 6

3

UNIT 2 VOCABULARY – CHAP 6

(2) THE NOTATION “P” REPRESENTS THE TRUE PROBABILITY OF AN EVENT HAPPENING, ACCORDING TO AN IDEAL DISTRIBUTION.

* THIS IS A PARAMETER: A SET, FIXED, CONSTANT VALUE WHICH IS SOMETIMES KNOWN AND SOMETIMES UNKNOWN, DEPENDING ON HOW COMPLICATED THE SPECIFIC PROBLEM IS.

* USUALLY, WE DON’T KNOW THE VALUE OF P, SO WE SOMETIMES TRY TO ESTIMATE IT WITH……

4

UNIT 2 VOCABULARY – CHAP 6

“P-HAT” , WHICH REPRESENTS AN EXPERIMENTAL PROBABILITY, OR ONE THAT COMES FROM A SET OF DATA INSTEAD OF AN IDEALIZED FORMULA.

* THIS IS A STATISTIC: A VARIABLE, NON-CONSTANT VALUE WHICH CHANGES EVERY TIME THE EXPERIMENT IS RUN OR THE DATA IS COLLECTED.

* SINCE P-HAT TAKES ON A SET OF VALUES, THESE CAN BE GRAPHED, JUST LIKE OTHER SETS OF NUMBERS.

* WE USUALLY RUN AN EXPERIMENT OR COLLECT A SET OF DATA SO THAT, WHEN WE CALCULATE THE VALUE OF THE STATISTIC, WE CAN USE THIS VALUE TO ESTIMATE THE TRUE VALUE OF THE ASSOCIATED PARAMETER.

5

UNIT 2 VOCABULARY – CHAP 6(3) The Sample Space of an event is the set of

all outcomes as measured by the definition of the variable we are assessing.

For example, if I flip a coin and am interested in recording which side is UP, then the sample space would be {heads, tails}.

On the other hand, if I flipped three coins and were interested in how many heads I get – recording this value as X – then the sample space would be {0,1,2,3}.

If I were interested in whether or not it would snow today, then the sample space would be {snows, doesn’t snow}.

6

UNIT 2 VOCABULARY – CHAP 6

(3) Sample Space, continued……• Not everything in the Sample Space

has to have the same probability of happening.

• However, the sum of all of the probabilities of the events in the sample space must add up to 1 (100%), since this is everything which is possible to happen.

7

UNIT 2 VOCABULARY – CHAP 6

(4) Probability Distribution > a table with all of the values that X can take (its sample space) and the probabilities of each of those values> the sum of all of the probabilities that are listed in a probability distribution should equal 100%

8

UNIT 2 VOCABULARY – CHAP 6

(5) Mutually Exclusive Events can’t happen at the same time. > “Disjoint” is another term for Mutually Exclusive> For example, if I roll a die, then the events “I get a multiple of 3” and “I get a multiple of 4” are mutually exclusive.

9

UNIT 2 VOCABULARY – CHAP 6

(5) (continued)

P (A or B) = P(A) + P(B) – P(A and B at the same time)

Note: If A and B are mutually exclusive, then they can’t happen at the same time.

Thus, P(A and B at the same time) would equal 0, right? So the formula would edit down to this: P (A or B) = P(A) + P(B)

10

UNIT 2 VOCABULARY – CHAP 6

(6) If I tell you ahead of time that I am somehow restricting the domain, then this will be a Conditional Probability.> Words that might alert you: “if”, “given”, “when”

Tricky formula:

Try not to use this formula all of the time; just use common sense!

( )( )

( )

P AandBP A B

P B

11

UNIT 2 VOCABULARY – CHAP 6

(7) Two events are called complements of each other if……* They are “opposite” of each other, and* Between the two of them, they make up the entire sample space, and* Their probabilities add up to 100%.

12

UNIT 2 VOCABULARY – CHAP 6

(7) (continued)For example, if I were to select a student at

random from this class, then “I pick a boy” and “I pick a girl” would be complementary.

Another example: if Ryan was shooting five free throws, then “he misses them all” and “he makes at least one shot” would be complements.

13

UNIT 2 VOCABULARY – CHAP 6

(8) INDEPENDENCE Informally, this refers to the outcome of

one event not having an influence on the outcome of another event.

Here it is, in more technical language: “Two events – A and B – are said to be independent if knowing that one occurs does not change the probability that the other occurs.”

14

INDEPENDENCE

(8) More Independence: There are two, equivalent formulas for

determining independence. The one you use depends on the individual problem you are doing:

15

INDEPENDENCE

(i) A and B are independent if and only ifP(A and B) = P(A) * P(B) (book pg

351)

(ii) A and B are independent if and only ifP(B given A) = P(B) (book pg 375)