Lecture 2: Review of probability

Question 1

What is the defintion of a discrete vs a continue random variable?

Answer 1

Question 2

What are the 3 (Kolmogorov) axioms of probability?

Answer 2

Question 3

What are the definitions of:
1. Probability of completement
2. probability of unions
3. mutally exclusive events?

Answer 3

Question 4

What is the defintion of an independent event?

Answer 4

Question 5

What is a Probability Distribution/Density Function (PDF)?

Answer 5

Question 6

What is a Cumulative Distribution Function (CDF)?

Answer 6

Question 7

Draw the PDF and CDF of height of men

Answer 7

Question 8

What is the formula of viariance? Derive this from first principles.

Answer 8

Question 9

What is the formula for skewness and Kurtois

Answer 9

Question 10

What is a Joint Probability Density Function?

Answer 10

Question 11

What is the marginal probability distributions of the following joint probability density function?

Answer 11

Question 12

What is the Bayes theorem?

Answer 12

Question 13

What is the definition and formula for covariance?

Answer 13

Question 14

What is the definition and formula for the correlation coefficient?

Answer 14

Question 15

What are the 3 properties of expected Value?

Answer 15

Question 16

What are the 5 properties of Variance and Covariance

Answer 16

Question 17

What is the Law of iterated Expectations?

Answer 17

Question 18

What is the definition and formula for conditional variance?

Answer 18

Question 19

What are the implications of independent

Answer 19

Question 20

What is a binomial distribution and what is it’s formula?

Answer 20

Question 21

What is the definition and formula for the poisson distribution

Answer 21

Question 22

What are the 3 properties of a normal distribution

Answer 22