Probability

Question 1

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Answer 1

Classical is when all outcomes have an equal chance of occuring, empirical is based on past events , and subjective is guesswork
past frequency divided by number of trials
Classical because the requirement usually isn’t met in the real world
Subjective

Question 2

What represents a sample space in probability
How to denote elements of a sample space
When are sample spaces disjoint
What does the conjunction fallacy say
Whats the complement of an event
Formula for complement
What is a stochastic process in probability theory
What is a state space in probability theory

Answer 2

S
With capitals
When they have no elements in common
The probability of two events happening is greater than the probability of either event
The chance of anything but the evnt happening
1-P(A) = P(A’)
A temporally indexed sequence of random variables
Same as the sample space for a static system and for a dynamic system A set of all possible states

Question 3

disjoint vs independent events
probability of either of two disjoint vs nondisjoint events
Conditional probability of two statistically independent events is —- from original
Formula for the conditional probability

Answer 3

Disjoint is mutually exclusive and independent is one does not affect the other
Disjoint is the sum of their individual probabilities and nondisjoint is the sum minus the joint probability
Different
P(AIB) = Probability of the intersection divided by the probability of the condition

Question 4

Formula for conditional probability
Multiplication rule of probability
Joint Probability of independent vs dependent events

Answer 4

P(AIB) is P(A (union) B) / P(B) or P(BIA) is P(B (union) A) / P(A)
P(A (union) B) is P(AIB) * P(B) or
P(A (union) B) is P(BIA) * P(A)
Independent is product and dependent is sum

Question 5

Joint probability
Marginal probability
conditional probability
Random experiment
Sample space
Birthday problem
Collectively exhaustive
Statistical independence

Answer 5

Probability of two events occurring simultaneously
The probability of an event irrespective of another variables probability
The probability of an event occurring in the presence of another
Anything with an uncertain outcome
All possible outcomes f a random experiment
How many people must be in a room for the probability of two having the same birthday to be over 50%
Property of a set where one of its constituents must happen
Property where an ccurance doesn’t influence another