Probability theory

Question 1

What is a sample space?

Answer 1

The set in which every element of a stochastic experiment is represented by exactly one element.

Question 2

What is an “Event”

Answer 2

a subset “E” of the sample space, representing a collection of favourable outcomes corresponding to that event

Question 3

What is an elementary event

Answer 3

When the set E only consists of one outcome

Question 4

What is a compound event?

Answer 4

When the set E consists of more than one outcome

Question 5

What is relative frequency

Answer 5

Consider a stochastic experiment with sample space 𝑆. The experiment is
repeated 𝑛 times, and on each trial an event of interest 𝐸 ⊆ 𝑆 occurs or doesn’t occur. The
relative frequency of the event, denoted 𝑟𝑓 (𝐸) is the number of times the event 𝐸 occurs 𝑛
divided by the number of repetitions (or trials), 𝑛.

Question 6

What is the probability of an event E

Answer 6

P(E) = lim n-> infinity r * Fn(E)

Question 7

What are the probability axioms

Answer 7

1 ) P(empty set) = 0
2) P(complement E) = 1 - P(E)
3) IEP theorem
4) 3 set IEP

Question 8

For any event E that is a subset of S, the probability of E is

Answer 8

abs(E)/k, where k is the number of outcome

Question 9

What’s the Probability of
P(E|F) + P(E^C|F)

Answer 9

= 1

Question 10

what is the multiplication theorem

Answer 10

P(E AND F) = P(E|F)P(F)

Question 11

What is the law of total probability?

Answer 11

P(A) = sum(P(A|Ei)P(Ei)

Question 12

What is bayes theorem

Answer 12

P(E|F) = P(F|E)P(E) (1/P(F))