Exam #2 - Chs. 4.4, 5, 6, 7

Question 1

simulation

Answer 1

technique used to recreate a random/unpredictable event
–> tactile or virtual
–> goal: measure how often some outcome occurs

Question 2

probability

Answer 2

long-term proportion of some outcome
–> Law of Large Numbers: as number of repetitions increases, proportion of an outcome approaches its probability

Question 3

experiment

Answer 3

any situation, that can be repeated, with uncertain results

Question 4

normal distribution

Answer 4

if a continuous random variable has a relative frequency histogram in the shape of the normal curve

Question 5

General Multiplication Rule

Answer 5

for any two events E and F, P(E and F) = P(E)*P(F|E)

Question 6

bell-shaped graphs?

Answer 6

for a fixed p value, as n increases, the distribution of data will become more bell-shaped
–> random variable X is approximately bell-shaped if np(1-p) ≥ 10

Question 7

combination

Answer 7

an unordered arrangement without replacement
–> number of arrangements of r objects from n objects, where r ≤ n and all n objects are distinct, = (nCr) = (n!)/(r!(n-r)!)

Question 8

standard deviation of binomial random variable

Answer 8

√(np(1-p))

Question 9

area under the curve

Answer 9

represents the proportion of the population with a characteristic within that interval
OR
probability of a randomly selected individual having a characteristic within that interval

Question 10

event (E)

Answer 10

any collection of outcomes
–> can be one or multiple
–> simple event (ei) represents only one outcome

Question 11

probability model

Answer 11

list of all possible outcomes and their probabilities for any given experiment

Question 12

probability density function (pdf)

Answer 12

equation used to measure probabilities for continuous random variables
–> total area under curve = 1
–> height of curve at all points ≥ 1

Question 13

permutation

Answer 13

an ordered arrangement without replacement
–> number of arrangements of r objects from n objects, where r ≤ n and all n objects are distinct, = (nPr) = (n!)/(n-r!)

Question 14

normal approximation to the binomial pdf

Answer 14

if np(1-p) ≥ 10, the binomial random variable X is approximately normally distributed, with a mean μ = np and standard deviation √(np(1-p))
–> to approximate probabilities, we must correct for continuity (add/subtract 0.5 from x value)

Question 15

standard deviation for discrete random variable

Answer 15

√(∑[(x-μ)^2P(x)]
= √(∑[x^2P(x)]-μ^2

Question 16

Classical (Theoretical) Approach

Answer 16

P(E) = (number of possibilities of E)/(number of total possibilities)
–> requires that all outcomes are equally likely

Question 17

rules of probability

Answer 17

–> for any event E, 0 ≤ P(E) ≤ 1
–> for S = {e1, e2…en}, P(e1) + P(e2) +…+ P(en) = 1

Question 18

associations between variables

Answer 18

as (x) changes, it becomes clear that (y) changes in some pattern
–> can help adjust predictions once made clear
–> relative frequencies for all categories, given some condition, will be equal if an association does not exist

Question 19

sample space (S)

Answer 19

collection of all possible outcomes

Question 20

Complement Rule for Z

Answer 20

area to the right of z = 1 - area to the left
–> can be used to find percentile rank (kth percentile is where k% of area is to the left)

Question 21

random variable

Answer 21

numerical measure of the outcome of a probability experiment (X)
–> discrete: finite/countable number of values
–> continuous: infinitely many values

Question 22

impossible probability

Answer 22

P(E) = 0

Question 23

independence

Answer 23

if occurrence of some event E does not affect the probability of occurrence for some event F
–> disjoint events are not independent - having one occur insinuates the other did not
–> two events E and F are independent if P(E|F) = P(E)

Question 24

conditional distribution

Answer 24

relative frequency of each value of a response variable for some specific value of explanatory variable
–> can show associations between variables

Question 25

properties of normal density curve

Answer 25

–> symmetric about the mean μ
–> single peak at x = μ (mean = median = mode
–> inflection points at x = μ-σ and x = μ+σ
–> area under curve = 1
–> area under curve to left of μ = 1/2 = area to right

Question 26

disjoint events

Answer 26

two events with no outcomes in common

Question 27

z α (z sub alpha)

Answer 27

z-score such that the area under the curve to the right of z = α (to the left, 1 - α)

Question 28

subjective probability

Answer 28

probability determined on the basis of personal judgment (can still be valid)

Question 30

General Addition Rule

Answer 30

for any two events E and F, P(E or F) = P(E) + P(F) - P(E and F)

Question 31

Multiplication Rule of Counting

Answer 31

if a sequence of choices has p options for the first choice, q options for the second choice, and r options for the third choice - and all options are independent, the number of possibilities = pqr

Question 32

Complement Rule

Answer 32

if E^c represents all outcomes in S that are not in some event E, P(E^c) = 1-P(E)

Question 33

inflection points

Answer 33

points where curvature of the graph changes; occur at x = μ-σ and x = μ+σ

Question 34

mean for discrete random variable

Answer 34

∑[x*P(x)]
–> mean value of n trials of the experiment will approach the overall mean as n increases

Question 35

binomial probability distribution

Answer 35

discrete probability distribution with two mutually exclusive outcomes (typically, success vs. failure)
–> fixed number of independent trials
–> each trial must have two disjoint or mutually exclusive outcomes
–> probability of success must be fixed for all trials

Question 36

random process

Answer 36

situation where the outcome of any particular trial is unknown, but proportion of observing that outcome approaches some value as the number of trials increases

Question 37

end behavior of normal curve

Answer 37

as x approaches positive and negative infinity, the graph approaches - but never reaches - the horizontal axis
–> probabilities computed as 0 are reported as < 0.001; computed as 1, reported as > 0.999

Question 38

conditional probability

Answer 38

P(F|E) = probability of F occurring, given that E has already occurred
–> if E and F are any two events, P(F|E) = (P(E and F))/(P(E))

Question 39

Addition Rule for Disjoint Events

Answer 39

if E and F are disjoint or mutually exclusive, P(E or F) = P(E) + P(F)

Question 40

mutually exclusive events

Answer 40

occurrence of one event prohibits the occurrence of the other

Question 41

marginal distribution

Answer 41

frequency or relative frequency distribution for the row/column variable
–> removes effect of other variable

Question 42

mean of binomial random variable

Answer 42

μ = np

Question 43

binomial random variable

Answer 43

when random variable X represents the number of successes in n trials
–> p = probability of success
–> (1-p) = probability of failure

Question 44

standard normal distribution

Answer 44

if the normal random variable X as a mean μ and standard deviation σ, it can be standardized to Z = (x-μ)/(σ)
–> Z has μ = 0 and σ = 1
–> table V gives areas under the normal curve for some value of z (z-score)

Question 45

Empirical (Experimental) Approach

Answer 45

P(E) ~ relative frequency of E
P(E) = (frequency of E)/(number of trials)

Question 46

binomial probability distribution function (pdf)

Answer 46

probability of x successes in n trials = nCxp^x(1-p)^n-x

Question 47

Simpson’s Paradox

Answer 47

when association between two variables inverts or disappears completely after a third variable is introduced

Question 48

certain probability

Answer 48

P(E) = 1

Question 49

unusual probability

Answer 49

P(E) < 0.05 (< 5%)

Question 50

Multiplication Rule for Independent Events

Answer 50

if E and F are independent, P(E and F) = P(E)*P(F)

Question 51

permutations with non-distinct items

Answer 51

if, of n objects, n1 are of some kind; n2 of some kind, and nk of a kth kind, the total number of arrangements = (n!)/([n1!][n2!][nk!]), where n = n1 + n2 + nk

Question 52

stacked/segmented bar graph

Answer 52

one bar for each value of explanatory variable –> split into proportions corresponding to each response

Question 53

contingency table

Answer 53

relates two categories of data (row and column variable)