Section 2

Question 1

How do you calculate the expectation of what is inside the E(“”) bracket?

Answer 1

Multiply it with the density function, then integrate

Question 2

Define variance?

Answer 2

Measure of dispersion about the mean

Question 3

What does covariance measure?

Answer 3

How 2 variables are associated with each other:
If +ve, then if X values increase Y would too and vice versa
If -ve, then if X values increase Y would decrease and vice versa

Question 4

Difference between covariance and correlation?

Answer 4

Correlation also tells us about the strength of the +ve or -ve relationship (not just direction)

Question 5

2 requirements so we can use a sample to estimate things about a population?

Answer 5

1) sample of data we use to be a representative sample

2) to use an estimator that has good properties

Question 6

What are sampling distributions and why do they occur?

Answer 6

Since estimators are functions of the random sample, and each Xi has been drawn from the same distribution, the estimators are also random variables and tf too have distributions

Question 7

What does the central limit theorem state?

Answer 7

That is a sample n is large, even if the underlying random sample has been picked from a distribution that is not a normal distribution, it will take ten form of a normal distribution

Question 8

For θ(hat) to be a good estimator of θ, what 3 properties must it exhibit?

Answer 8

1) unbiasedness: tf E(θ) = θ
2) efficiency: variance must be small tf more precise estimator
3) consistency: a large sample, or asymptotic property; as n->infinity, the variance of the estimator must tend to 0 until the density collapses to a single spike at θ

Question 9

Define type 1 error?

Answer 9

The error of rejecting a null hypothesis that is actually true (happens α% of the time)

Question 10

Define type 2 error?

Answer 10

Error of not rejecting a null hypothesis that is actually false

Question 11

What is the size of a test?

Answer 11

α - the probability of making a type 1 error

Question 12

What is the power of a test?

Answer 12

The probability of not committing a type 2 error - ie. Probability of rejecting a false hypothesis

Question 13

What are IIDs?

Answer 13

Independently and identically distributed random variables

Means each observation has been drawn independently from the same distribution so each Xi has the same distribution