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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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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