Homework  - Conditional Probability & Bayesian Analysis

1) Questions:

a. Consider rolling a 6 sided die 100 times to determine the number of times a "1" occurs:

i. This is an example of what type of probability?

ii. What is the "sample space" for this problem?

iii. Give an example of an "element" of this sample space.

iv. What would the "Random Variable" be?

b. What are each of the following and how are they related: PMF, PDF, CDF?

c. What is a conditional probability? How is it represented symbolically? What is a joint probability? How is it represented symbolically? How are joint probabilities related to conditional probabilities?

d. What conditional probability relationship holds for correlated events? What conditional probability relationship holds for mutually exclusive events?

e. What is Bayes' Theorem (formula)? What does it permit you to do?

Other Potential Test Questions:

1) What is P(AUB)? What does it mean?

2) What is P(A∩B)? What does it mean?

3) What does it mean for two events to be independent or dependent? How is this expressed symbolically in terms of joint probabilities and conditional probability?

4) What does it mean for two events to be mutually exclusive? How is this expressed symbolically in terms of joint probabilities and conditional probability?

5) What does it mean for two events to be correlated? How is this related to the concept of independence/dependence? What is the difference between correlation and causation?

6) What is Bayes' Theorem (formula)? What does it permit you to do?

7) Define each of the following: 1) a priori probability, 2) marginal probability, 3) a posteriori probability, and 4) likelihood.

8) How is the marginal probability related to the likelihoods and the a priori probabilities?

9) Define the following in terms of conditional relationships: true positive, false positive, true negative, false negative. How are they related?