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Stats 14-17
stats.
30
Mathematics
12th Grade
12/13/2011

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Term
Law of Large Numbers
Definition
guarentee that long-run relative frequency of repeated independent events settles down to true probability as the number of trials increases
Term
something has to happen rule vs. compliment rule
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))
Term
AND / OR
Definition
both need to occur at the same time, intersection, Ω
/
either or, union, normal U
Term
multiplication rule (AND)
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)
Term
Addition Rule (OR)
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)
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
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
Term
conditional probability (and equation)
Definition
probability that takes into account a given condition such as "B given A"

P (B|A) = P (A Ω B) / P(A)
Term
how to find independent
Definition
P(A) = P (A|B) or vise versa
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
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(+)
Term
HOW TO CREATE TABLE: survey 995 adults: 81.5% over 30. 36.8% snore. 32% of all respondents are snorers over 30.
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
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"
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
Term
when to create venn diagram vs. table vs. tree diagram
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
Term
HOW TO ADDRESS PROBLEM:
84 17 year olds contacted: 73 respond
275 20 year olds contacted: 225 respond
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)
Term
triple ven diagram to solve:
-P (A and B)
-P (A|C)
Definition
-doesn't matter if C is involved too (and = intersection = both at same time = Ω)
-P (A and C) / P(C)
Term
random variable
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)
Term
calculate expected value and standard deviation of probability table
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...
Term
variance
Definition
expected value of squared deviations (just square root it to get the standard deviation)
Term
MEAN:
-X+Y
-X-Y
-X1+X2
-3X
-2X-Y
-Y-2
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
Term
STANDARD DEVIATION
-X+Y
-X-Y
-X1+X2
-3X
-2X-Y
-Y-2
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
Term
why doesnt X1+X2+X3 = 3X?
Definition
each X represents a situation not the same variable, so X1+X2+X3 is 3 times of the same event, not one event.
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
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
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
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
Term
what determines bernouli trial
Definition
- only 2 outcomes
- constant sucess rate p
- independent events
Term
The success/failure condition
Definition
a binomial model is approximately Normal if we expect at least 10 sucesses and 10 failures (np, nq) > or = 10
Term
discrete vs. continuous random variables
Definition
discrete have only certain outcomes (1, 3, 5, 7) where continuous is like the normal model where any real number can be it
Term
how to read MINITAB (3 things)
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)
Term
GEOM/BINOMIAL:
-how to find between 7 and 11 (15 trials)
-how to find between (inclusive) 5 and 9 (15 trials)
Definition
-cdf(10)-cdf(7)
-cdf(9)-cdf(4)
Term
BINOMIAL PDF
-small n
-large n
GEOMETRIC PDF
CUMULTIVE DISTRIBUTIONS (CDF)
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%)
Term
(n)
(k) or nCk

-what is it / what does it represent
Definition
n!/k!(n-k)! ... represents how many combinations of k successes there are in n trials
Term
"is it fair?"
Definition
compare amount they pay to mean amount they get paid (expected # they would get paid)
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