5) Sampling and Convergence

Question 1

What is a random sample of size n from a distribution Fx

Answer 1

Question 2

What is the sample mean

Answer 2

Question 3

What are the expectation and variance of the sample mean

Answer 3

Question 4

What is Markov’s inequality

Answer 4

When Y is a non-negative random variable.

Question 5

What is Markov’s inequality for when Y can take negative values

Answer 5

Question 6

What is the inequality for the probability that ∣Y∣≥a for a random variable Y

Answer 6

Question 7

What is Chebyshev’s inequality

Answer 7

Question 8

What is Chebyshev’s inequality in terms of standard deviation

Answer 8

Question 9

What does it mean for the sequence of random variables X1, X2, . . . converges in probability to X as n → ∞

Answer 9

Question 10

What is the Weak law of large numbers

Answer 10

Question 11

What does it mean if the sequence of random variables X1, X2, . . . converges in distribution to X as n → ∞

Answer 11

Question 12

What is the Central limit theorem (CLT)

Answer 12

Question 13

What are some of the key remarks regarding CLT

Answer 13

Question 14

What is the continuity theorem for mgfs

Answer 14

Question 15

How do you express the limx→a f(x)/g(x) = 0

Answer 15