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MA223—Elementary Probability & Statistics > Exam 2 > Flashcards

Exam 2 Flashcards

1
Q

probability

A

quantifies long-term randomness

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2
Q

law of large numbers

A

as n increases, proportion of occurrences of a given outcoe approaches a particular number

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3
Q

relative frequency

A

large number of trials to find long run proportion of outcomes

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4
Q

probability experiment

A

chance process leading to well-defined outcomes

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5
Q

outcome

A

result of a trial of a probability experiment

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6
Q

sample space

A

set of all possible outcomes

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7
Q

event

A

subset of a sample space

corresponds to a particular outcome or group of outcomes

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8
Q

3 basic interpretations of probability

A

classical
empirical (relative frequency)
subjective

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9
Q

complement

A

set of all outcomes not included in event

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10
Q

intersection of 2 events

A

outcomes in 2 different events

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11
Q

union of 2 events

A

outcome in one event or the other

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12
Q

disjoint events

A

do not have any common outcomes

mutually exclusive

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13
Q

conditional probability

A

reduction of sample space by imposing a condition

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14
Q

2 ways to check if two events are independent

if either are true, they are independent

A
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15
Q

fundamental counting rule

A

in a sequence of n events in whcih the first has k1 possibilities, the second has k2 and so on, the total number of possibilities of the sequence will be

k1k2k3…kn

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16
Q

sensitivity

A

p(POS|S)

positive test given state present

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17
Q

specificity

A

p(NEG|S^c)

negative test given state not present

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18
Q

permutation

A

arrangement of objects in a specific order

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19
Q

combination

A

grouping of objects where order does not matter

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20
Q

random experiment

A

function that assigns a numerical value to each simple event in a sample space

21
Q

the random variable reflects…

A

the aspect of the experiment that is of interest to us

22
Q

X refers to…

A

random variable itself
(ex. number of heads in 3 coin flips)

23
Q

x refers to…

A

a possible value of the random variable

24
Q

probability distribution

A

specifies a random variable’s possible values and their respective probabilities

25
Q

standard deviation formula for probability distribution

A
26
Q

4 requirements for binomial distribution

A
  1. fixed number of trials, n
  2. each trial has only 2 outcomes, success or failure
  3. outcomes must be independent
  4. probability of success must be the same for each trial
27
Q

poisson used for…

A

rare events
events occurring over time

28
Q

lambda

A

rate
adjust for interval given

29
Q

for poisson, rate = lambda = ? = ?

A

rate = lamda = mean = variance

30
Q

format for hypergeometric distribution

A
31
Q

explain hypergeometric distribution

A

distribution of a variable that has 2 outcomes when sampling is done without replacement

32
Q

for hypergeometric,

x = 0, 1, 2, 3…min(….)

A

x = 0,1,2,3…min(a, n)

33
Q

explain geometric distribution

A

an experiment with 2 outcomes that is repeated until a success

34
Q

for geometric,

x =

A

number of trials until first success

35
Q

shape parameter for normal distribution

A

standard deviation

36
Q

shift/location parameter for normal distribution

A

mean

37
Q

empirical rule: 1 standard deviation away

A

68% of data
16% on either side

38
Q

empirical rule: 2 standard deviations away from mean

A

95% of data
2.5% on either side

39
Q

empirical rule: 3 standard deviations away from mean

A

99.7% of data
0.15% on either side

40
Q

unique to standard normal distribution

A

mean = 0
standard dev = 1

41
Q

arguments for normalcdf

A

normalcdf(-10,000, x, 0, 1) = area

42
Q

arguments for invNorm

A

invNorm(area, 0, 1) = z

43
Q

sampling distribution

A

probability distribution that specifies probabilities for the possible values a statistic can take

44
Q

sampling distribution helps predict…

A

how close a statistic falls to the parameter it estimates

45
Q

mean and standard deviation trend for samples

A
46
Q

formula for standard deviation of sample

A
47
Q

standard error

A

standard deviation of sample

48
Q

as sample size increases…

A

standard error decreases

49
Q

central limit theorem

A

sampling distribution is always normal if n ≥ 30, no matter the shape of the original distribution

(also works sometimes with a smaller n)

MA223—Elementary Probability & Statistics (3 decks)

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