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25 Cards in this Set
- Front
- Back
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rare event rule
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given a particular assumption, if the probability of an observed event is extremely rare, we conclude that the assumption is probably not correct
ie) Flip coin and should be .5 of heads or tails. If it appears .9 tails and .1 heads, our assumption of coin being fair was probably wrong. |
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event
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a collection of outcome with a specific rule
ie) all outcome having 2 heads and 1 tail are HHT HTH THH |
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simple event or sample point
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one possible outcome that can't be broken down to simpler components.
ie) HTH |
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sample space (S)
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the set of all possible outcomes from a procedure; all simple events
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notation of an event
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Defining an event-
A:{obtaining 2 heads and 1 tail} (or) A:{HHT, HTH, THH} Probability of an event P(A)=0.375 |
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probability (rule 1)
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the proportion of times a specific outcome would occur over the long run experimentally
P(A)= (# of ways A occured)/(# of times trial is repeated) |
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relative frequency
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the number of times an outcome would occur relative to other outcomes
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probability (rule 2)
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the proportion of times a specific outcome occurs theoretically
P(A)= (# of ways A can occur)/(# of possible simple events) P(A)= S/n |
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law of large numbers
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as a procedure is repeated many times, the relative frequency probability (from rule 1) of an event tends to approach the actual probability (from rule 2)
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personal probability of an event (rule 3)
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the degree to which an individual believes the event will happen (aka subjective probability)
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compound events
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a composition of two or more other events
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union (A ∪ B)
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occurs if either A or B both occur on a single performance of an experiment
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intersection (A ∩ B)
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event that occurs if both A and B occur on a single performance of the experiment
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disjoint or mutually exclusive events
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if two events have no outcomes in common (no intersections)
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complementary events
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the event that A does not occur
denoted by A_bar or A^c P(A) + P(A_bar) = 1 |
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calculating possible outcomes of all events
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(# of possible samples)^(# of samples per event)
ie) toss a coin 10 times. # of possible samples = 2 (H or T) # of samples per event = 10 possible outcomes = 2^10 = 1,024 |
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additive rule of probability
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P(A∪B) = P(A) + P(B) - P(A∩B)
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conditional probability
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the probability that event A occurs given that event B occurs
P(A|B) |
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independent events
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when event B does not alter the probability that event A has occurred
P(A|B) = P(A) P(A∩B) = P(A)P(B) (otherwise known as dependent events) |
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Given deck of 52 cards:
1. What is probability that the first card is a heart? 2. What is the probability that the second card is spade? 3. What is the probability that the first card is a heart and the second card is a spade? 4. Given that the first card is a heart, what is the probability that the second card is a spade? |
1. 13/52
2. 13/52 (didn't specifically say "considering the first card is a heart") 3. (13/52)(13/51) 4. 13/51 |
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combinations rule
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number of different samples containing r elements that can be selected from n elements
|n| = (n!)/(r!(n-r)!) |r| |
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permutations rule
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number of different ordered samples containing r elements that can be selected from n elements
n_P_r = (n!)/(n-r)! |
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Bayes Rule
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what to do when you want to go from P(A|B) --> P(B|A)
P(B¹|A) = P(B¹)P(A|B¹) / [P(B¹)P(A|B¹)+P(B²)P(A|B²)+...] |
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prior probability (considering Bayes Rule)
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the probability of a certain event before considering how other events effect it
Bayes Rule: P(B¹|A) = P(B¹)P(A|B¹) / [P(B¹)P(A|B¹)+P(B²)P(A|B²)+...] P(B¹) is prior probability |
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posterior probability (considering Bayes Rule)
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the probability of a certain event given that another event has occurred
Bayes Rule: P(B¹|A) = P(B¹)P(A|B¹) / [P(B¹)P(A|B¹)+P(B²)P(A|B²)+...] P(B¹|A) is posterior probability |
