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2017-2018 AP STATS > EOYR Unit 4 vocab > Flashcards

EOYR Unit 4 vocab Flashcards

1
Q

probability this AND that . Add or multiply?

A

MULTIPLY

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2
Q

What is “mutually exclusive?”

A

same as disjoint

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3
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

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4
Q

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

A

binocdf(12, p, 5)

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5
Q

Give three examples of independent variables

A
  1. Being tall and having a high GPA2. If it is snowing and whether it is a Thursday or not3. 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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6
Q

How do you find mean and sd of probability model?

A

put values in L1, probabilities in L2, and run “1-var stats L1,L2” and you get it!

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7
Q

what is n! ?

A

it is “n factorial” example: 5! = 54321= 120. tells you how many ways you can arrange n objects.

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8
Q

What is the expected value?

A

The mean of the random variable. What you’d AVERAGE if you played the game A LOT!!!!!!!!!

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9
Q

What is probability first success is on 7th try?

A

qqqqqq p (q^6*p). (this is a GEO prob)

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10
Q

binopdf

A

(n,p,x). Probability of exactly X successes in N trials. (PARTICULAR probability)

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11
Q

What is the “mean of a random variable?”

A

The expected value. sum of probs times values

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12
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

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13
Q

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

A

(6 or more)

1 - binocdf(12, p, 5)

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14
Q

what do we call it when events are not associated?

A

independent

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15
Q

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

A

1 - p(NONE)
not zero, not zero or less
1-binopdf(12, p, 0)

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16
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).

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17
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: 3y sd sqrt (3z2) var 3z2

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18
Q

How to find P(at least 1)?

A

1-P(none)

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19
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

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20
Q

How can we use Pascal’s Triangle?

A

To find probability of x successes in K trials.. BINOMIAL BABY!!!

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21
Q

what does binomial model tell us about?

A

exactly x successes in K trials. What is likelihood of exactly 3 heads out of 13 flips?

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22
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)

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23
Q

when can you expect the first success? (mean of GEO) if ther3 is a 30 percent chance?

A

1/p? or 1/.30?. Which is 3.333 so around the 3rd or 4th try.
This tells you, on average, when the first success will occur

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24
Q

What is the area under the normal curve?

A

1 or 100%

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25
Q

what is probability?

A

THE LONG RUN RELATIVE FREQUENCY!!

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26
Q

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

A

(more than 4)

1 - binocdf(12, p, 4)

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27
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? or DISJOINT EVENTS ARE ALWAYS ASSOCIATED!!

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28
Q

what is pythagorean theorem of stats?

A

st dev of combined model is: sqrt(st dev squared + st dev squared) or more if you combine more?

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29
Q

what does geometric model tell us about

A

it is about FIRST SUCCESS? What is likelihood first success is on 5th trial?

30
Q

How to make TREES with screening tests????

A

SPLIT UP POPULATION FIRST&raquo_space;»» then split the groups by outcomes of the test

31
Q

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

A

independent events

32
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

33
Q

What do we call it when events are not independent?

A

associated

34
Q

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

A

binopdf(12,p,5)

35
Q

Give three examples of disjoint events

A
  1. A card being a CLUB and a RED2. A student being a SENIOR and a FRESHMAN3. An animal being a CAT and a GOLDFISH(both can’t be true)
36
Q

Probability of THIS OR THAT?

A

ADD P(this) + P(that) works when disjoint only, when not, subtract overlap.

37
Q

what is a complement?

A

the probability that it doesn’t happen. 1-P(it happens). (together they add to 100%)

38
Q

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

A
  1. Playing video games and gender (Knowing male makes itmore likely theyplay)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).
39
Q

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

A

probability A times probability B (knowing A is true) called general multiplication ruleP(A)P(B given A)P(this)P(that given this)

40
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) called “general addition rule”P(A)+P(B)-P(A and B)P(this)+P(that)-P(this and that)

41
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

42
Q

geopdf

A

(p,x)? probability of FIRST SUCCESS being ON the Xth trial

43
Q

How many ways can I arrange 4 letters?

A

4!432*1= 24 ways

44
Q

binocdf

A

(n,p,x)?.. Probability of X OR LESS successes in N trials. (CUMULATIVE probability)

45
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.

46
Q

Give three examples of events that are not mutually exclusive

A
  1. Being a DOG and being SMELLY2. Being a FRESHMAN and being FEMALE3. Liking ICE CREAM and liking HAMBURGERS(both can be true simultaneously)
47
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.

48
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?.

49
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

50
Q

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

A

disjoint OR mutually exclusive

51
Q

Probability of THIS AND THAT?

A

MultiplyP(this)*P(that) works when independent only, when not, then P(that) should be p (that|this)

52
Q

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

A

not on the 4th or before

1-geocdf(p, 4)

53
Q

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

A

Geocdf(p, 5)

54
Q

What is area under ANY probability curve?

A

1 (or 100%)

55
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.

56
Q

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

A

(4 or less)

binocdf(12, p, 4)

57
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..

58
Q

what is disjoint?

A

can’t be joined?. They can’t both happen at the same time! (being over 5 feet and under 4 feet)

59
Q

what is independent? 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.

60
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

61
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 VAR –> var: 9z2+25c2

62
Q

When to use general add 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)(IT ALWAYS WORKS IN ALL SITUATIONS, when disjoint, P(this and that)= 0, so you end up with the simpler disjoint version)

63
Q

geocdf

A

ON OR BEFORE

(p,x). Probability of the FIRST SUCCESS being ON OR BEFORE the Xth trial.

64
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.

65
Q

What is diff between 3X and X+ X+ X (finding sd)

A

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

X+X+X is playing 3 times, square SD, add 3 times, sqrt.

66
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 sqr (z2+c2) var z2+c2

67
Q

how do you combine probability models? (play more than one game)

A

add or subtract the means, and then ADD THE VARIANCES ALWAYS?

68
Q

When to use general mult 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)

69
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.

70
Q

Do we say things are “dependent?”

A

NO! we say associated

2017-2018 AP STATS (15 decks)

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