Populations To Samples

Question 1

Describe the process of sampling from a population

Answer 1

• The population is driven by an rv X. Even though we may know the distribution, we may not know the parameters involved.
• We select a random sample X₁,…X_n which are I.I.D rvs from the same distribution as X. The joint pmf or pdf is equal to the product of the individual pmf or pdf
• From the sample available, we compute similar quantities to the unknown parameters, (eg x̄, s²)
• The population quantities are numbers. The sample quantities (also known as estimators or statistics) are random variables

Question 2

Define the Chi-squared distribution with 1 degree of freedom

Answer 2

Question 3

Define the Chi-squared distribution with v degrees of freedom

Answer 3

Question 4

Define the student’s t-distribution

Answer 4

Question 5

Define the F-distribution

Answer 5

Question 6

Define the 100p% quantile

Answer 6