Exam 2

Question 1

probability

Answer 1

quantifies long-term randomness

Question 2

law of large numbers

Answer 2

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

Question 3

relative frequency

Answer 3

large number of trials to find long run proportion of outcomes

Question 4

probability experiment

Answer 4

chance process leading to well-defined outcomes

Question 5

outcome

Answer 5

result of a trial of a probability experiment

Question 6

sample space

Answer 6

set of all possible outcomes

Question 7

event

Answer 7

subset of a sample space

corresponds to a particular outcome or group of outcomes

Question 8

3 basic interpretations of probability

Answer 8

classical
empirical (relative frequency)
subjective

Question 9

complement

Answer 9

set of all outcomes not included in event

Question 10

intersection of 2 events

Answer 10

outcomes in 2 different events

Question 11

union of 2 events

Answer 11

outcome in one event or the other

Question 12

disjoint events

Answer 12

do not have any common outcomes

mutually exclusive

Question 13

conditional probability

Answer 13

reduction of sample space by imposing a condition

Question 14

2 ways to check if two events are independent

if either are true, they are independent

Answer 14

Question 15

fundamental counting rule

Answer 15

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

Question 16

sensitivity

Answer 16

p(POS|S)

positive test given state present

Question 17

specificity

Answer 17

p(NEG|S^c)

negative test given state not present

Question 18

permutation

Answer 18

arrangement of objects in a specific order

Question 19

combination

Answer 19

grouping of objects where order does not matter

Question 20

random experiment

Answer 20

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

Question 21

the random variable reflects…

Answer 21

the aspect of the experiment that is of interest to us

Question 22

X refers to…

Answer 22

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

Question 23

x refers to…

Answer 23

a possible value of the random variable

Question 24

probability distribution

Answer 24

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

Question 25

standard deviation formula for probability distribution

Answer 25

Question 26

4 requirements for binomial distribution

Answer 26

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

Question 27

poisson used for...

Answer 27

rare events events occurring over time

Question 28

lambda

Answer 28

rate adjust for interval given

Question 29

for poisson, rate = lambda = ? = ?

Answer 29

rate = lamda = mean = variance

Question 30

format for hypergeometric distribution

Answer 30

Question 31

explain hypergeometric distribution

Answer 31

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

Question 32

for hypergeometric, x = 0, 1, 2, 3...min(....)

Answer 32

x = 0,1,2,3...min(a, n)

Question 33

explain geometric distribution

Answer 33

an experiment with 2 outcomes that is repeated until a success

Question 34

for geometric, x =

Answer 34

number of trials until first success

Question 35

shape parameter for normal distribution

Answer 35

standard deviation

Question 36

shift/location parameter for normal distribution

Answer 36

mean

Question 37

empirical rule: 1 standard deviation away

Answer 37

68% of data 16% on either side

Question 38

empirical rule: 2 standard deviations away from mean

Answer 38

95% of data 2.5% on either side

Question 39

empirical rule: 3 standard deviations away from mean

Answer 39

99.7% of data 0.15% on either side

Question 40

unique to standard normal distribution

Answer 40

mean = 0 standard dev = 1

Question 41

arguments for normalcdf

Answer 41

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

Question 42

arguments for invNorm

Answer 42

invNorm(area, 0, 1) = z

Question 43

sampling distribution

Answer 43

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

Question 44

sampling distribution helps predict...

Answer 44

how close a statistic falls to the parameter it estimates

Question 45

mean and standard deviation trend for samples

Answer 45

Question 46

formula for standard deviation of sample

Answer 46

Question 47

standard error

Answer 47

standard deviation of sample

Question 48

as sample size increases...

Answer 48

standard error decreases

Question 49

central limit theorem

Answer 49

sampling distribution is always normal if n ≥ 30, no matter the shape of the original distribution (also works sometimes with a smaller n)