Stats def from book

Question 1

Define central limit theorem

Answer 1

Question 2

State Law of total Probabilty

Answer 2

Question 3

What is the ‘power’ of a statistical test

Answer 3

Question 4

Define Sample mean

Answer 4

Question 5

State details for testing a proportion against a given value

Answer 5

Question 6

State axioms of probabilitiy

Answer 6

Question 7

Define expectation and Var of Uniform Random Variable

Answer 7

Question 8

Define MSE and define and derive formula relating to var and bias

Answer 8

Question 9

What is an unbias estimator and what is the bias of an estimator

Answer 9

Question 10

When is something positively skewed/negatively skewed

Answer 10

Question 11

Defn of Discrete Random Variable

Answer 11

Question 12

State and prove result for the expectation of a sum of random variables with joint probability

Answer 12

Question 13

define type I error and type II error

Answer 13

Question 14

What is an estimator

Answer 14

Question 15

Define uniform distribution and its pdf

Answer 15

Question 16

Define F distribution

Answer 16

Question 17

Expectation and Variance of (negative) exponential dist.

Answer 17

Question 18

State details testing mean against given value, variance unknown

Answer 18

Question 19

State details for testing mean against a given value, variance known

Answer 19

Question 20

Define moment generating function

Answer 20

Question 21

State result for conditional expectation

Answer 21

Question 22

Define how we find the mode of a continious random variable and a discrete random variable

Answer 22

Question 23

Describe the jist behind a geometric distribution

Answer 23

Question 24

Defn of Gamma function

Answer 24

Question 25

Eqn of median of a function in terms of cumlitive distribution

Answer 25

Question 26

Define Coefficiant of variance

Answer 26

Question 27

State Expectation and Var of Negative Binomial Distribution

Answer 27

Question 28

State the strong law of large numbers

Answer 28

Question 29

Conditions for function f(x) to be a pmf (continous case)

Answer 29

Question 30

state expectation and variance of hypergeometric distribution

Answer 30

Question 31

Define joint probability mass function

Answer 31

Question 32

Define beta distribution and its pdf (include beta function)

Answer 32

Question 33

State and prove iterated expeectation law

Answer 33

Question 34

State Expectation, Variance and derive PGF of Geometric distribution

Answer 34

Question 35

Define rth moment about alpha

Answer 35

Question 36

Define Chi squared distribution

Answer 36

Question 37

What is expectation and variance of sample mean of IID

Answer 37

Question 38

Defn of mutually independent events

Answer 38

Question 39

What is sampling distribution and what is standing error

Answer 39

Question 40

Define Expectation of continous random variable

Answer 40

Question 41

State details of Geometric distribution and its pmf

Answer 41

Question 42

defn of pooled estimator

Answer 42

Question 43

Define normal distribution and its pdf

Answer 43

Question 44

Define a random Variable

Answer 44

Question 45

Define joint distribution function

Answer 45

Question 46

Define confidence interval for \mu with signicance level \alpha

Answer 46

Question 47

Define PGF

Answer 47

Question 48

Whats expecation and variance of normal dist

Answer 48

Question 49

State details of negative binomial distribution

Answer 49

Question 50

State details testing equality of means, variance known

Answer 50

Question 51

Describe jist of hypergeometric

Answer 51

Question 52

Define conditional probability distribution and its pdf

Answer 52

Question 53

What distribution is the chi squared distribution the same as, and what is its mean and variance

Answer 53

Question 54

State details testing equality of of two variances

Answer 54

Question 55

Defn of (Negative) Expotential Dist. and its pmf

Answer 55

Question 56

State Properties of Cumlative Distribution Function

Answer 56

Question 57

define sample variance

Answer 57

Question 58

State and prove result for the variance of the sum of independent random variables

Answer 58

Question 59

Define beta function

Answer 59

Question 60

Defn of independence of variables for joint probability functions

Answer 60

Question 61

(operational) state defn of independence of continious random variables

Answer 61

Question 62

State details of Hypergeometric distribution and its pmf

Answer 62

Question 63

State result about the mgf of independent random variables

Answer 63

Question 64

state details for testing dependent means

Answer 64

Question 65

Define t- distribution

Answer 65

Question 66

Gamma dist and its pdf

Answer 66

Question 67

Define a continous random variable

Answer 67

Question 68

State result which suppose X has a distribution and Y =g(X), to find the pdf of Y.

Answer 68

Question 69

state pdf for multinominal dist

Answer 69

Question 70

state conditional density of X\_1 given X\_2

Answer 70

Question 71

Give two eqns for Var(X)

Answer 71

Question 72

What is Expectation and variance of beta distribution

Answer 72

Question 73

State MGF of normal distribution and describe how you would derive it.

Answer 73

Question 74

State details for testing two proportions are equal

Answer 74

Question 75

Summary table of 'time till accident' type which distribution for discrete and continious

Answer 75

Question 76

Describe jist of negative binomial dist.

Answer 76

Question 77

Define consistent

Answer 77

Question 78

what is pgf of sum of independent random variables

Answer 78

Question 79

State details testing variance against a given value

Answer 79

Question 80

State and prove iterated expectation law

Answer 80

Question 81

State Bayes Theorem

Answer 81

Question 82

Define null hypothisis and alternative hypothisis

Answer 82

Question 83

Expectation and Var of gamma distribution

Answer 83

Question 84

State result about the expectation of independant random variables of X\_1, X\_2. E(X\_1 \* X\_2)

Answer 84

Question 85

State details testing equality of two means, variance unknown but equal

Answer 85

Question 86

State defn of independence which holds for both discrete and continious cases

Answer 86

Question 87

Describe jist of poisson distribution

Answer 87

Question 88

Expectation of a function defn

Answer 88

Question 89

Define Expectation of a discrete variable

Answer 89

Question 90

What is Observed Sig level (p -value

Answer 90

Question 91

State and Prove Generalised Multiplication Law

Answer 91

Question 92

State details testing equality of two means, variance unknown and unequal

Answer 92

Question 93

Define poisson dist. and its pmf

Answer 93

Question 94

Cumilative distribution for a Uniform Distribution

Answer 94