1) Overview of Statistical Learning

Question 1

What is an exponential family

Answer 1

A set of probability distributions expressed as - (where where 𝑏(𝑥) is the base density, 𝒖(𝑥) the canonical statistics, and 𝜼 the canonical parameters)

Question 2

What is an empirical estimator

Answer 2

An empirical estimator 𝜃ˆ is obtained by substituting the true distribution 𝐹 with the empirical distribution 𝐹ˆ𝑛, constructed from observed data, to estimate a functional 𝜃 = 𝑔(𝐹) as 𝜃ˆ = 𝑔(𝐹ˆ𝑛)

Question 3

What is the emperical estimate of the mean and variance

Answer 3

Question 4

What is the likelihood function

Answer 4

Question 5

What is the pmf, expectation and variance of the geometric distribution

Answer 5

Question 6

What is the pmf, expectation and variance of the exponential distribution

Answer 6

Question 7

What is the pmf, expectation and variance of the binomial distribution

Answer 7

Question 8

What is the pmf, expectation and variance of the poisson distribution

Answer 8