Quant Test 2

Front 1

independent event (172)

Back 1

event a is independent of event b if the conditional property p(A|B) is the same as the unconditional probability p(a).

Front 2

multiplication law for independent events (173)

Back 2

total probability is the product of independent probabilities

Front 3

fundamental rule of counting (182)

Back 3

if event a can occur in n1 ways and event b can occur in n2 ways, then events a and b can occur in n1 * n2 ways.

Front 4

factorials (182)

Back 4

the number of ways that n items can be arranged in a particular order

n!=n(n-1)(n-2)...1

example: number of ways to arrange 9 baseball players for batting

9!=9*8*7*6*5*4*3*2*1= 362,880

Front 5

permutations (183)

Back 5

arrangement of the r sample items in a particular order

ORDER MATTERS

nPr= n!/(n-r)!)

Front 6

combinations (183)

Back 6

arrangement of r items chosen random from n items where order is NOT important

nCr= n!/(r!(n-r)!)

Front 7

stochastic process (193)

Back 7

repeatable random experiment

Front 8

probability models (193)

Back 8

depict essential characteristics of a stochastic process to guide decisions or make predictions

Front 9

random variable (193)

Back 9

function or rule that assigns numerical value to each outcome in the sample space of a random experiment,

X= random variable in general
x1, x2...= specific values of X

Front 10

discrete random variable (193)

Back 10

countalbe number of distinct values

Front 11

discrete probability distribution (194)

Back 11

assigns a probability to each value of a discrete random variable x.

probability for any given value of X (xi) must be between 0 and 1

sum of all xi's must be equal to 1

Front 12

expected value (195, ex 196)

Back 12

E(X)=mu=sum of each occurance 8 the probability of that occurance

Front 13

variance of a discrete random sample (197)

Back 13

sigma squared=sum of the squared deviations about its expected value, weighted by the prob of each x value

sum of [xi-mu]^2 *p(xi)

Front 14

standard deviation of a discrete random sample (197)

Back 14

square root of variance

Front 15

PDF (198)

Back 15

graphical display of the probability for each value

Front 16

CDF (198)

Back 16

graphical display of the cumulative sum of probabilities

Front 17

uniform distribution (199)

Back 17

desribes random variable with a finite number of integer values from a to b

a=lower limit
b= upper limit

Front 18

PDF (200) uniform discrete distribution

Back 18

P(x)=1/(b-a+1)

Front 19

range (200) uniform discrete distribution

Back 19

a <| x <| b (for integer x only

Front 20

standard deviation (200) uniform discrete distribution

Back 20

squre root of ([(b-a) +1)]^2 - 1)/12

Front 21

bernoulli experiment (203)

Back 21

experiment that has only 2 outcomes

sucess x=1
failur x=0

pi= denotion of the probability of success

Front 22

binomial distribution (204)

Back 22

where bernoulli experiment is repeated n times

Front 23

paramter of binomial experiment (205)

Back 23

n=number of trial
pi= probability of success

Front 24

PDF (205)

Back 24

P(x)=n!/(x!(n-x)!) * pi^x * (1-pi)^n-x

Front 25

PDF excel function (205)

Back 25

=binomdist(x,n,pi,0 or 1)

0= pdf
1= cdf

Front 26

range (205)

Back 26

x=1,2,...n

Front 27

mean (205)

Back 27

n*pi

Front 28

standard deviation (205)

Back 28

square root of n*pi(1-pi)

Front 29

binomial shape (205)

skwewed right
symmetric
skewed left

Back 29

pi < .5
pi= .5
pi>.5

Front 30

compounds events (208)

Back 30

add individual probabilites to obtain any desired event probability.

Front 31

poisson process (212)

Back 31

# of occurences within a randomly chosen unit of time (minute, hour) or space (square foot, mile)

Front 32

paramter of poisson distribution (213):

lamda

Back 32

mean arrivals per unit of time or space

Front 33

paramter of poisson distribution (213):

PDF

Back 33

P(x) = (lamda^x * e^-lamda)/X!

Front 34

paramter of poisson distribution (213):

range

Back 34

x=0,1,2...(no obvious upper limit)

(number of people)

Front 35

paramter of poisson distribution (213):

mean

Back 35

lamda

Front 36

paramter of poisson distribution (213):

standard deviation

Back 36

square root of lamda

Front 37

paramter of poisson distribution (213):

skewness

Back 37

always right skewed, but less so for larger lamda

Front 38

paramter of poisson distribution (213):

excel function

Back 38

=poisson(x,lamda,cumulative)

0=PDF
1=CDF

Front 39

discrete variable (227)

Back 39

each value of x has its own probability p(x)

Front 40

continous varialbe (227)

Back 40

impossible to speak of probability at that point

Front 41

intervals (227)

Back 41

probabilities are areas underneath smooth curves

Front 42

uniform continuous distribution (229)

Back 42

x is a random variable that is uniformly distributed between a and b, its pdf has constant height.

Front 43

uniform continuous distribution (230):

parameters

Back 43

a- lower limit
b- upper limit

Front 44

uniform continuous distribution (230):

PDF

Back 44

f(x)=1/(b-a)

Front 45

uniform continuous distribution (230):

CDF

Back 45

p(X<=x)=(x-a)/(b-a)

Front 46

mean

Back 46

(a+b)/2

Front 47

uniform continuous distribution (230):

standard deviation

Back 47

sqrt((b-a)^2/12)

Front 48

uniform continuous distribution (230):

shape

Back 48

symmetric with no mode

Front 49

normal/gaussian distribution (232)

Back 49

symmetric, bell shaped distribution

Front 50

normal distribution (232):

parameters (mu, sigma)

Back 50

mu= population mean
sigma=population standard deviation

Front 51

normal distribution (232):

PDF

Back 51

see equation p 232

Front 52

normal distribution (232):

range

Back 52

-infinity >>infinity

Front 53

what is "normal"? (234)

Back 53

measured on continous scale
posses clear central tendency
have only 1 peak (unimodal)
exhibit tapering tails
be symmetric about the mean (equal tails)

Front 54

standardized variable for a population (235)

Back 54

z=(x-mu)/sigma

Front 55

standard normal distribution (235)

Back 55

see page 235

Front 56

finding normal areas with excel (241)

normal distribution

Back 56

=normdist(x,mu,sigma, cumulative)

area to the left of x

Front 57

finding normal areas with excel (241)

normal inverse

Back 57

=norminv(area,mu,sigma)

value of x corresponding to given left tail area.

Front 58

finding normal areas with excel (241)

normal standardized distribution

Back 58

=normsdist(z)

area to the left of z in a standard normal

Front 59

finding normal areas with excel (241)

normal standardized inverse

Back 59

value of z corresponding to given left tail area.

Front 60

exponential distribution (251)

Back 60

event per unit of time follow a poisson distribution. focuses on waiting time until the next event.

Front 61

characteristics of exponential distribtion (251):

lambda

Back 61

mean arrival rate per unit of time or space

Front 62

characteristics of exponential distribtion (251):

PDF

CHECK

Back 62

e^((-lambda)(x))

Front 63

characteristics of exponential distribtion (251):

CDF

Back 63

1-e^((-lambda)(x))

Front 64

characteristics of exponential distribtion (251):

mean

Back 64

1/lambda

Front 65

characteristics of exponential distribtion (251):

stdev

Back 65

1/lambda

Front 66

characteristics of exponential distribtion (251):

shape

Back 66

always right skewed

Front 67

characteristics of exponential distribtion (255):

excel function

Back 67

=expondist(x,lambda,1)

1=CDF (left of tail area)
0=height of PDF

Front 68

sample statistic (263)

Back 68

random variable whose value depends on which population items happen to be included in a random sample

Front 69

sampling variation (263)

Back 69

variation of results based on the subjects of the test.

Front 70

estimator (265)
estimate (265)

Back 70

statistic derived from a sample to infer the value of a population parameter.

value of the estimator in a particular shape

Front 71

sampling distribution (265)

Back 71

probability distribution of all possible values the statis may assume when a random sample of size n is taken

Front 72

sampling error (265)

equation

Back 72

differene between an estimate theta hat and the corresponding population theta.

sample error= thetha hat - theta

theta hat= estimator
theta=population parameter

Front 73

bias (265)

equation

Back 73

difference between the expected value of the estimator and the true parameter

bias=e*theta hat -theta

Front 74

sampling erros vs biased error (266)

Back 74

sampling error is random while bias is symmetric

theta hat=estimate
theta=population parameter

Front 75

efficiency (267)

Back 75

vairance of the estimators sampling distribution. smaller varaiance means a more efficient estimator

Front 76

consistent estimator (267)

Back 76

convergres toward the parameter being estimated as the sample size increases.

as n increases, data is to become more accurate

Front 77

standard error of the mean (268)

equation

Back 77

sampling error of the sample mean is described by its standard deviation

standard error of mean=stdev/square root of sample size

Front 78

point estimate (276)

Back 78

sample mean x bar is a point estimate of the population mean mu

Front 79

confidence interval (276)

confidence level

Back 79

specified probability of containing mu.

probability that the confidence interval contains the true mean is usually expressed as a percentage.

Front 80

confidence interval for mu with known standard deviation (276)

confidence level and z

Back 80

x bar +- z(stdev/sqrt n)

90-1.645
95-1.960
98-2.326
99-2.576

Front 81

student's t distribution

Back 81

used when population is normal but its standard deviation is unknown. used instead of z distribution. particularly important when sample size is small.

Front 82

degrees of freedom (280)

formula

Back 82

used to determine the value of the t statistic used in the confidence interval formula.

v (aka nu)=n-1

Front 83

mean of uniform discerete distribution (200)

Back 83

(a+b)/2