Chapter 5

Question 1

What is the law of large numbers?

Answer 1

As the sample size n increases to infinity…
…the sample mean becomes the expected value (random variable mean)

Question 2

What is the central limit theorem?

Answer 2

As the sample size n increases to infinity…

Question 3

What is another way to right the formula in terms of the sum of the independent random variables?

Answer 3

Question 4

What does the Law of Large Numbers tell us and what does the Central Limit Theorem tell us?

Answer 4

-the law of large numbers tells us the sample mean is close to u
-the central limit theorem tells us how close sigma/(sqrt(n)) is to N(0,1)

Question 5

What is a binomial random variable?

Answer 5

the sum of Bernoulli random variables

Question 6

What is the normal approximation to the binomial?

Answer 6

Question 7

Provide an example of the continuity correction

Answer 7

Question 8

Provide an example of the continuity correction

Answer 8

Question 9

When do you use the continuity correction?

Answer 9

-when you are summing discrete random variables
-you do not do it when you are summing continuous random variables

Question 10

How big does n have to be for the normal approximation to be valid?

Answer 10