Term
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Definition
| guarentee that long-run relative frequency of repeated independent events settles down to true probability as the number of trials increases |
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Term
| something has to happen rule vs. compliment rule |
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Definition
| probability of set of all possible outcomes must = 1 vs. probability of an event occurring is 1-probaility that it doesn't occur (P(a) = 1-P(A^c)) |
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Term
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Definition
both need to occur at the same time, intersection, Ω
/
either or, union, normal U |
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Term
| multiplication rule (AND) |
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Definition
IF 2 INDEPENDENT EVENTS:
P (A Ω B) = P(A) x P(B) (x P(C), etc for any number of events needing to occur)
DON'T NEED INDEPENDENCE:
P (A Ω B) = P(A) x P(B|A) |
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Term
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Definition
P (A U B) = P(A) + P(B) - P(A Ω B)
-if 2 disjoint events (no outcomes in common) then you can ignore the last term, but also remember that if they are independent you can substitute P(A) x P(B) in for
P (A Ω B) |
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Term
78% test(A), 36% quiz(B), 22% both:
-what venn diagram looks like
-how to find both
-how to find either but not both
-how to find neither |
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Definition
-A is 78-22, B is 36-22, 22 is in middle, .08 is outside
-just A + just B + middle (or using addition rule you add total A including middle, total B including middle, then subtract middle percentage out ONCE)
-just A + Just B
-Just outside |
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Term
| conditional probability (and equation) |
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Definition
probability that takes into account a given condition such as "B given A"
P (B|A) = P (A Ω B) / P(A) |
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Term
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Definition
| P(A) = P (A|B) or vise versa |
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Term
P (false positive) = .01. P(having TB) = .0005.
P(false negative) = .001
-what tree diagram looks like
-how to find probability of each occurring
-how to find probability of having TB if you get a positive test |
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Definition
-first branch is actually TB or actually not TB, 2nd branch is what each test said for actually TB and not TB
-probability of occurance: multiply each line of branches together
-P(having TB | +) so P(TB and +) / P(+) |
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Term
| HOW TO CREATE TABLE: survey 995 adults: 81.5% over 30. 36.8% snore. 32% of all respondents are snorers over 30. |
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Definition
put total COUNTS not percentages (multiply percentages by 995):
995 in corner, make box with snore/non snore on x and over 30/under 30 on y
total over 30: .815(995)
total under 30: reciprocal of over
total snore: .368(995)
total not snore: reciprocal of snore
snorer and over 30: .32(995)
then the rest can be filled in |
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Term
thing to remember:
-rollling dice ... P(sum of 8 or doubles)
-picking card ... P(heart or ace)
-having children
-"risen from 69% reached to 76% reached" |
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Definition
-sample space includes 2then1 and 1then2 (idk why, fuck it!)
-OR means only one intersection so you need to subtract ace of hearts
-usually just write out sample space
-doesn't frickin' matter, just use current one for reached and 1-76 for not reached |
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Term
| when to create venn diagram vs. table vs. tree diagram |
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Definition
venn diagram for this, that, and both.
you can always start with a tree diagram in confusing problems, and need it for something with more than 4 possibilities (19 or 20, blood test or no blood test, breathalizer or no breathalizer)
table good for everything that has 4 possibilities |
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Term
HOW TO ADDRESS PROBLEM:
84 17 year olds contacted: 73 respond
275 20 year olds contacted: 225 respond |
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Definition
make a frickin' table!!!
label x 17 or 20 and y respond or don't respond
total 17 year olds:84
total 20 year olds:275
total people respond: 73+225
total people not respond: opp. of ^
17 and respond: 73
20 and respond: 225
(non respond = opp of above) |
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Term
triple ven diagram to solve:
-P (A and B)
-P (A|C) |
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Definition
-doesn't matter if C is involved too (and = intersection = both at same time = Ω)
-P (A and C) / P(C) |
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Term
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Definition
| value based on outcome of a random event that is paired with a probability in a probability table (usually use X to signify it, so X=x means X=some number) |
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Term
| calculate expected value and standard deviation of probability table |
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Definition
expected value: do weighted average (make sure probabilities add up to 1)
standard deviation: SQROOT: (deviation of x1 from mean)^2(probability 1) x (deviation of x2 from mean)^2(probability 2) etc... |
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Term
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Definition
| expected value of squared deviations (just square root it to get the standard deviation) |
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Term
MEAN:
-X+Y
-X-Y
-X1+X2
-3X
-2X-Y
-Y-2 |
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Definition
-mean of X + mean of Y
-mean of X - mean of Y
-mean of X + mean of X
-3 x mean of X
-2 x mean of X - mean of Y
-mean of Y - 2 |
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Term
STANDARD DEVIATION
-X+Y
-X-Y
-X1+X2
-3X
-2X-Y
-Y-2 |
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Definition
-SQROOT:SD^2 of x + SD^2 of y (must be independent, or it will be 0!)
-SQROOT: SD^2 of x + SD^2 of y (must be independent!)
-SQROOT: SD^2 of x +SD^2 of x (must be independent!)
-3 x SD of X
-SQROOT: SD^2 of 2X + SD^2 of Y (must be independent!)
-SAME SD AS Y |
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Term
| why doesnt X1+X2+X3 = 3X? |
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Definition
| each X represents a situation not the same variable, so X1+X2+X3 is 3 times of the same event, not one event. |
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Term
GEOMETRIC BERNOULI TRIAL:
-what p and q represent
-how to write out work
-how to put into calculator
-how to find expected number of trials until success (mean) and standard deviation |
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Definition
- p = success, q = failure
- 3rd try: p^1 x q^2
at most 2: (p^1) + (p^1 x q^1)
no less than 4: 1-(at most 3) OR q^n where n=1 less than it can be
-geompdf (p, # of tries) or geomcdf (p, at most # of tries)
-expected #: 1/p
standard deviation: SQROOT: q/p^2 |
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Term
BINOMIAL BERNOULI TRIAL:
-what p, q and n represent
-how to write out work
-how to put into calculator
-how to find expected number of trials until success (mean) and standard deviation |
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Definition
- p = success, q = failure, n=# of trials
- 3 successes in 5 trials: 5C3 x p^3 x q^2
at most 2: 5C0 + 5C1 + 5C2
no less than 4: 1 - (at most 3)
-binomialpdf (n, p, # of successes) or binomialcdf (n, p, at most # of successes)
-expected # (mean): np
standard deviation: SQROOT: npq |
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Term
| what determines bernouli trial |
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Definition
- only 2 outcomes
- constant sucess rate p
- independent events |
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Term
| The success/failure condition |
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Definition
| a binomial model is approximately Normal if we expect at least 10 sucesses and 10 failures (np, nq) > or = 10 |
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Term
| discrete vs. continuous random variables |
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Definition
| discrete have only certain outcomes (1, 3, 5, 7) where continuous is like the normal model where any real number can be it |
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Term
| how to read MINITAB (3 things) |
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Definition
-check if PDF/CDF or geometric/binomial
-next to writing is number of trials and success rate
-left column is x like you would plug into binomial () or geom(), right column is probability for each (so pretty much its doing the annoying calculator work for you) |
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Term
GEOM/BINOMIAL:
-how to find between 7 and 11 (15 trials)
-how to find between (inclusive) 5 and 9 (15 trials) |
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Definition
-cdf(10)-cdf(7)
-cdf(9)-cdf(4) |
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Term
BINOMIAL PDF
-small n
-large n
GEOMETRIC PDF
CUMULTIVE DISTRIBUTIONS (CDF) |
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Definition
BINOMIAL PDF
-p<.5 = skewed right
p=5 = mound shaped
p>.5 = skewed left
-all mound shaped
GEOMETRIC PDF
skewed right
CUMULITIVE DISTRIBUTIONS (CDF) skewed left (last bar always 1 aka 100%) |
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Term
(n)
(k) or nCk
-what is it / what does it represent |
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Definition
| n!/k!(n-k)! ... represents how many combinations of k successes there are in n trials |
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Term
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Definition
| compare amount they pay to mean amount they get paid (expected # they would get paid) |
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