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2017-2018 AP STATS > ALL UNIT 4 > Flashcards

ALL UNIT 4 Flashcards

1
Q

major difference between bino and geo?

A

BINO is about a number of successes

GEO is all about when the FIRST SUCCESS happens

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2
Q

what is the big difference between PDF and CDF?

A

The PDF’s are EXACTLY,

so exactly 5 successes (binopdf),

or first success exactly on the seventh try (geopdf).

CDF’s are CUMULATIVE (added up),

so 5 OR LESS successes (binocdf)

or the first success ON OR BEFORE the seventh try (geocdf)

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3
Q

binocdf vs geocdf

A

both cumulative

(added up probabilities)

binocdf tells you P(X OR LESS successes… )

geocdf tells you P(First success ON OR BEFORE…. )

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4
Q

binocdf vs binopdf

A

cdf is cumulative

it tells you “x or less successes”

pdf is not

it tells you “exactly x successes”

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5
Q

geocdf vs geopdf

A

geocdf is cumulative

it tells you “first success ON OR BEFORE the xth try”

geocdf is exact

it tells you “first success exactly ON the xth try”

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6
Q

binopdf vs geopdf

A

both are pdf

(both not cumulative)

binopdf tells P(EXACTLY X successes)

geopdf tells P(FIRST SUCCESS ON… )

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7
Q

binopdf

binocdf

geopdf

geopdf

A

binopdf: EXACTLY x successes in N tries
binocdf: X OR LESS successes in N tries
geopdf: FIRST SUCCESS on the xth try
geocdf: FIRST SUCCESS ON OR BEFORE the xth try

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8
Q

Give three examples of independent variables

A
  1. Being tall and having a high GPA
  2. If it is snowing and whether it is a Thursday or not
  3. Whether a person likes pizza and their gender

(notice, knowing one bit of information does not impact the likelihood of the other being true also)

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9
Q

When to use general mult rule and what is it?

A

AND probability.

Use when associated.

P(this)*P(that|this).

IT ALWAYS WORKS FOR ALL SITUATIONS. When indep, the P(that|this) = P(that). So you end up with the simpler independent version: P(this)*P(that)

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10
Q

If combining 4 random variables with standard deviations of m, p, q, r….

What is the new combined standard deviation?

A

SQRT(m2 + p2 + q2 + r2)

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11
Q

RAND VARIABLE:

X has mean y and standard deviation of z.

A has mean b and standard deviation c.

Find: Mean, SD and VAR of: X + X + X

A

mean: y+y+y
sd: SQRT(z2+z2+z2) ….
var: (z2+z2+z2)

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12
Q

what is independence?

What are the two equations to test for independence?

A

when P(A)=P(A|B) OR P(A)*P(B)=P(A and B)

When the probability of A is the same even when B is also true.

Knowing B does not affect the probability of A.

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13
Q

what does geometric model tell us about?

A

THE FIRST SUCCESS

Like, what is likelihood first success is on 5th trial?

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14
Q

What is the area under the normal curve?

A

1 or 100%

The area under any probability curve is 1.00

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15
Q

How many ways can I arrange 4 letters?

A

4!

4*3*2*1= 24 ways

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16
Q

Give three examples of variables that are not independent (associated)

A
  1. Playing video games and gender (Knowing male makes it more likely they play)
  2. Whether it is snowing and the month you are in (some months are more rainy than others, knowing what month changes likelihood of snowing)

3 If a pet is a dog and if it is a cat (knowing it is a dog makes it certain that it is not a cat).

(notice, knowing one bit of information changes the likelihood of the other being true also).

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17
Q

what is that (n over k) thing in the binomial equation?

A

n choose k

it tells you how many ways you can choose k objects from a set of n things.

The formula is n!/(n!(n-k)!)

the two numbers on bottom add to the number up top.

These are coefficients in expanded binomials and can also be found in Pascal’s Triangle

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18
Q

What is the “mean of a random variable?”

A

The expected value.

What you expect to win or get, on average, if you play once.

sum of (probabilities times values)

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19
Q

when can you expect the first success always?

as an example, if there is a 30 percent chance of success?(mean of geo)

A

1/p

(this is the mean of the geo model)

1/.30. Which is 3.333 so around the 3rd or 4th try.

1/p tells you, on average, when the first success will occur

1/p is the mean of the geometric distribution

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20
Q

what is representative?

A

It means that the sample statistics will be kind of like the population parameters..

The sample “looks like” the population.

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21
Q

Probability of THIS AND THAT?

A

Multiply

P(this)*P(that) works when independent only,

when not, then

P(this)*P(that|this)

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22
Q

What type of probability when you are looking for at least one success in twelve attempts?

A

AT LEAST ONE IS ALWAYS 1 - p(NONE)

Or think of simply not zero

1-all failures

1-qqqqqqqqqqqq

1-q12

1-binopdf(12, p, 0)

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23
Q

What is the “hot hand?”

A

a misinterpretation of the law of large numbers. Using this law, if you flipped 4 tails in a row, you’d expect the next one to be another tails, because tails is “hot.” A baseball player who gets three hits in a row, you expect another hit? wrong. Streaks happen randomly.

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24
Q

How many ways can you choose 3 books to take with you on a trip out of the 7 books on the shelf?

A

7 choose 3.

7! / (3! * 4!)

notice that the two factorials on bottom add to the top.

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25
Q

what is n! ?

A

it is “n factorial”

example: 5! = 5*4*3*2*1= 120.

tells you how many ways you can arrange n objects.

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26
Q

What type of probability when you are looking for more than 5 successes in twelve attempts?

A

BINO. (notice it is not a “first success” scenario)

6 or more same as not 5 or less

1 - binocdf(12, p, 5)

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27
Q

what does binomial model tell us about?

A

exactly x successes in K trials.

Like, what is likelihood of exactly 3 heads out of 13 flips?

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28
Q

what is probability?

A

THE LONG RUN RELATIVE FREQUENCY!!

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29
Q

How do you find mean and sd of discreet random variable ? (like if you have a table of values and probabilities?)

A

put values in L1, probabilities in L2

then run “1-var stats L1,L2” and you get it!

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30
Q

What type of probability when you are looking for exactly 5 or less successes in twelve attempts?

A

BINOMIAL

binocdf(12, p, 5)

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31
Q

how do you combine probability models?

(play more than one game)

A

add or subtract the means,

and then ADD THE VARIANCES

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32
Q

How to make TREES with screening tests????

A

SPLIT UP POPULATION FIRST >>>>>>

then split the groups by outcomes of the test

33
Q

can independent events be disjoint?

EXPLAIN

A

NO, if they are independent, then knowing one doesn’t change the probability of the other, but if they are disjoint, knowing one makes the other impossible, so it does change the probability of the other to 0

34
Q

Do we say things are “dependent?”

A

NO!

we say associated

35
Q

Probability this OR that when they are not disjoint?

How?

A

probability A plus probability B minus the double counted

(the ones that are both A and B)

This is called “general addition rule”

P(A)+P(B)-P(A and B)

P(this)+P(that)-P(this and that)

36
Q

probability this and that when they are not independent? How?

A

probability A times probability B (knowing A is true) called general multiplication rule

P(A)*P(B given A)

P(this)*P(that given this)

37
Q

What type of probability when you are looking for the first success after the fifth attempt?

A

GEOMETRIC cumulative

same as “not on the 4th or before”

1 - geocdf(p, 4)

38
Q

What do we call it when two things can’t happen at the same time?

A

disjoint OR mutually exclusive

39
Q

What type of probability when you are looking for less than 5 successes in twelve attempts?

A

BINOMIAL

same as 4 or less

bino function only does __ or less,

binocdf(12, p, 4)

40
Q

geopdf (inputs)

What does it tell you and what are the inputs?

A

FIRST SUCCESS ON

geopdf (p,x) will tell you

probability of FIRST SUCCESS being ON the Xth trial

41
Q

Give three examples of events that are not mutually exclusive

A
  1. Being a DOG and being SMELLY
  2. Being a FRESHMAN and being FEMALE
  3. Liking ICE CREAM and liking HAMBURGERS

(both can be true simultaneously)

42
Q

RAND VARIABLE:

X has mean y and standard deviation of z.

A has mean b and standard deviation c.

Find: Mean, SD and VAR of: 5A

A

mean: 5b
sd: 5c
var: 25c2

43
Q

probability this AND that . Add or multiply?

A

MULTIPLY

if indep.. just P(this)*P(that)

if associated then

P(this)*P(that | this)

44
Q

What is it called when knowing one event happened does not change the probability of another event occuring?

A

independent events

45
Q

RAND VARIABLE:

X has mean y and standard deviation of z.

A has mean b and standard deviation c.

Find: Mean, SD and VAR of: 3X

A

mean: 3y

SD 3z

var 9z2

46
Q

What is more important, percent of population or size of sample?

A

Sample size. A sample of 150 will say as much about a population of 2,000 as it will about a population of 2,000,000. The sample size determines level of confidence and interval widths..

47
Q

Why is it called “binomial”

A

These numbers come from the coefficients of expanded binomials..

(x+y)1, (x+y)2, (x+y)3

48
Q

what is pythagorean theorem of stats?

A

you can think of the sd of the models as legs of triangle, then the combined sd would be the hypotenuse.

st dev of combined model is:

SQRT( sd2 +sd2)

or more if you combine more

49
Q

What is “mutually exclusive?”

A

same as disjoint

can’t happen at the same time

50
Q

can disjoint events be independent?

EXPLAIN

A

NO..

If they are disjoint then knowing one tells you that the other couldn’t happen so they are always NOT INDEPENDENT.

DISJOINT EVENTS ARE ALWAYS ASSOCIATED!!

51
Q

Give three examples of disjoint events

A
  1. A card being a CLUB and a RED
  2. A student being a SENIOR and a FRESHMAN
  3. An animal being a CAT and a GOLDFISH(both can’t be true)
52
Q

What is the expected value?

A

The mean of the random variable.

What you would expect if you played just once, but it is actually

What you’d AVERAGE ON EACH TRY if you played the game A LOT!!!!!!!!!

53
Q

What is area under ANY probability curve?

A

1 (or 100%)

54
Q

what is a complement?

A

the probability that it doesn’t happen.

complement of M is NOT M,

or 1-P(M)

1-P(it happens).

(together they add to 100%)

55
Q

what is disjoint?

A

can’t be joined.

They can’t both happen at the same time!

also known as mutually exclusive

(being over 5 feet and under 4 feet)

56
Q

What type of probability when you are looking for exactly 5 successes in twelve attempts?

A

EXACTLY would be a bino

(notice it is not a “first success” scenario)

binopdf (12,p,5)

57
Q

What is probability first success is on 7th try?

A

qqqqqq p

(q^6*p).

or.. geopdf(p,7)

(this is a GEO prob, notice it says “first success”)

58
Q

binocdf (inputs)

What are inputs and what does it tell us?

A

EXACTLY X OR LESS successes in N tries (cumulative)

binocdf(n,p,x)..

Probability of X OR LESS successes in N trials.

(CUMULATIVE probability)

59
Q

How to find likelihood of being pregnant, given the test says you are? (tree)

A

Split population by %pregnant and % not who take test, then each of those into what test says.

Then look just the groups that the test said pregnant.

Then find: %pregnant/(total percent in both groups).

60
Q

Probability of THIS OR THAT.

Add or Multiply?

A

ADD

P(this) + P(that) works when disjoint only,

when not, subtract overlap.

61
Q

what do we call it when events are not associated?

A

independent

62
Q

What type of probability when you are looking for exactly 5 or more successes in twelve attempts?

A

BINOMIAL cumulative (notice no mention of “first”)

same as (more than 4)

Which is like “NOT 4 or less”

1 - binocdf(12, p, 4)

63
Q

binopdf(inputs)

what are inputs and what does it tell us?

A

EXACTLY X successes in N tries

binopdf(n,p,x).

Probability of exactly X successes in N trials.

(PARTICULAR probability)

64
Q

How to find P(at least 1)?

A

1-P(none)

65
Q

RAND VARIABLE:

X has mean y and standard deviation of z.

A has mean b and standard deviation c.

Find: Mean, SD and VAR of: X + A

A

mean: y+b

SD SQRT(z2+c2)

var z2+c2

66
Q

What type of probability when you are looking for the first success on or before the fifth attempt?

A

GEOMETRIC (first) cumulative

Geocdf(p, 5)

67
Q

How many successes can you expect?

(mean of binormial)

A

np.

Makes sense,

if 30% like butter, out of 50 people

you would expect (50)(.3)= 15 to like butter

np is the mean of the binomial distribution

68
Q

what is the law of large numbers?

A

states that in the long run.. (NOT SHORT RUN) The relative frequency settles down to true probability. (you’ll have 50% heads after an infinite number of coin flips with a fair coin)

69
Q

RAND VARIABLE:

X has mean y and standard deviation of z.

A has mean b and standard deviation c.

Find: Mean, SD and VAR of: 3X + 5A

A

mean: 3y+5b
sd: SQRT(9z2+25c2)
var: 9z2+25c2 (same as (3z)2 + (5z)2)

70
Q

What is the law of averages?

A

a misinterpretation of the law of large numbers.

Using this law, if you flipped 4 heads in a row, you’d expect the next one to be a tails because it should even out in the long run. Not true, 5 flips is not the long run. Infinity is. The next flip still has a 50% chance of being another head. You may hear someone say “he’s do for a hit” or “it’s bound to rain soon” both bad.

71
Q

RAND VARIABLE:

X has mean y and standard deviation of z.

A has mean b and standard deviation c.

Find: Mean, SD and VAR of: X + 12

A

mean: y+12

SD z

var: z2

72
Q

When to use general addition rule and what is it?

A

OR probability.

Use when not disjoint. (subtract overlap)

P(this OR that) = P(this)+P(that) - P(this and that)

73
Q

Do we add or subtract st dev when combining models?

A

neither you always just add variances. Square the st devs, add them, then take sqrt.

74
Q

What is diff between 3X and X+ X+ X

when combining random variable

(mean and st. dev)

A

3X is just tripling one play. Mult mean and SD by 3.

X+X+X is playing 3 times, must add variances, square SD’s add 3 times then sqrt.

75
Q

RAND VARIABLE:

X has mean y and standard deviation of z.

A has mean b and standard deviation c.

Find: Mean, SD and VAR of: 3X + 5A + 12

A

mean: 3y+5b+12
sd: sqrt (9z2 +25c2)

var 9z2+25c2

76
Q

What do we call it when events are not independent?

A

associated

77
Q

geocdf (inputs)

what does it tell us and what are inputs

A

FIRST SUCCESS ON OR BEFORE

geocdf(p,x).

Probability of the FIRST SUCCESS being ON OR BEFORE the Xth trial.

78
Q

What can Pascal’s Triangle tell you?

A

Binomial probability

Getting exactly X successes in N tries

2017-2018 AP STATS (15 decks)

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