Probability

Question 1

Define the types of probability
Formula for empirical
Which type is the most useless and why
Which type is the most useful

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

What is the probability of two disjoint events
When are events statistically independent
What is the probability of two statistically independent events
What is the probability of two nondisjoint events
Formula for the conditional probability

Answer 3

The sum of their individual probabilities
When their conditional probability is different from their original
The product of their individual probabilities
The probability of either ofthe sum of the individual probabilities minus the intersection
P(AIB) = Probability of the intersection divided by the probability of the condition

Question 4

Formula for conditional probability
Multiplication rule of probability
Probability of the intersection of two statistically independent 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)
P(A (union) B) is P(B) * P(A)

Question 5

Joint probability
Marginal probability
conditional probability
Random experiment
Sample space
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
Property of a set where one of its constituents must happen
Property where an ccurance doesn’t influence another