midterm 1

Question 1

how do determine if two events are independent

Answer 1

if P(A|B) = P(A)

Question 2

calculate sd of 12, 15, 9, 18

Answer 2

1. find the mean (12 + 15 + 9 + 18)/4 = 13.5
2. find each values deviation from mean and square it
   (12 - 13.5) ^2 + (15 - 13.5)^2 …..
3. for a sample, divide by n - 1

Question 3

find the 65th percentile of 900, 1000, 1300, 1700

Answer 3

1. use formula (4(n) + 1)(.65) = 3.25
2. third largest 1300 + (1700-1300) * .25

Question 4

permutation

Answer 4

use when order matters n!/(n-k)!

Question 5

combination

Answer 5

use when order does not matter n!/k!(n-k)!

Question 6

P(A U (or)B)

Answer 6

means probability that at least one event occurs A or B P(A) + P(B) - P(AnB)

Question 7

P(AnB)

Answer 7

means probability that both events occur
if independent P(A) x P(B)
if dependent P(A and B) = P(A|B)P(B)

Question 8

bayes law P(A|B)

Answer 8

predicting posterior probability
(P(B|A) * P(A) ) / P(B)

Question 9

nominal

Answer 9

categorizes data without inherent order - eye color / blood type

Question 10

ordinal

Answer 10

ordered categories - income level (low/middle/high)

Question 11

interval

Answer 11

numerical data

Question 12

chebysheffs theoreom

Answer 12

how much of the data lies withing k standard deviations
1 - 1/k^2

Question 13

covariance formula

Answer 13

E(XY) - E(X)E(Y)

Question 14

expected value with n and p

Answer 14

n * p

Question 15

variance using n and p

Answer 15

n * p(1-p)

Question 16

relationship between standard deviation and variance

Answer 16

sd is the sq root of variance

Question 17

covariance[X,Y]

Answer 17

E[XY] - E[X]E[Y]

Question 18

Variance

Answer 18

σ = sqrt(σ2)

Question 19

E(c) =

Answer 19

c - expected value of a constant is a constant

Question 20

E(X + c)

Answer 20

E(X) + c

Question 21

E(cX)

Answer 21

cE(X)

Question 22

V(c) =

Answer 22

0

Question 23

V(X + c)

Answer 23

V(X)

Question 24

V(cX)

Answer 24

c^2V(X)

Question 25

E(X+Y)

Answer 25

E(X) + E(Y)

Question 26

V(X+Y) ( independent)

Answer 26

V(X) + V(Y) + 2COV(X,Y)

Question 27

V(X+Y) dependent

Answer 27

V(X) + V(Y)

Question 28

ρ(X,Y)

Answer 28

COV(X,Y) / sdx sdy

Question 29

sample covariance

Answer 29

(x - xbar)(y-ybar) / n-1

Question 30

correlation of coefficient

Answer 30

sxy/sx * sy