Common Probability Distributions

Question 1

Define random variable

Answer 1

A quantity whose future outcomes are uncertain (stock returns)

Question 2

Define outcome

Answer 2

a possible value of a random variable (4.3%)

Question 3

Define event

Answer 3

a specified set of outcomes A = (rp < 10%) B = (rp >= 10%)

Question 4

What are the two defining properties of probability?

Answer 4

Property 1: the probabilities are mutually exclusive (if one happens, another can’t)
Property 2: the probabilities are exhaustive (covers all possible outcomes)

Question 5

Can event be impossible P(E) = 0% or certain P(E) = 100%?

Answer 5

No, they wouldn’t be random and would be constants.

Question 6

What are the three ways probabilities are estimated?

Answer 6

1) Empirical
2) Subjective
3) a priori

Question 7

What is the definition of the EMPIRICAL way of estimating probabilities?

Answer 7

• Estimation is base on historical observation(s)
• Past is assumed to be representative of the future
• Historical period must include occurrences of the event

Question 8

What is the definition of the SUBJECTIVE estimation probabilities?

Answer 8

The way of estimating probabilities by adjusting an empirical probability based on intuition or experience.

Used when there is a lack of empirical observations

Essentially, it’s when you make a personal assessment

Will the stock market go up or down in the next year?

Question 9

What is the definition of A PRIORI estimation probabilities?

Answer 9

Arriving at a conclusion based on deductive reasoning (e.g. rolling a six-sided dice, P(1) = 1/6