Week 1 Class 2- Probability

Question 1

What are the 2 basic rules of probability?

Answer 1

The prob of any event occurring is greater that 0 and less than or equal to 1
The sum of probs for all possible outcomes of an activity must =1

Question 2

What are the two main types of probability

Answer 2

Objective Approach

Subjective Probability

Question 3

Objective approach includes

Answer 3

Relative Frequency and Classical/ logical method

Question 4

Relative frequency

Answer 4

P(event) = # of occurrences of the event/ total # of trials or outcomes

Question 5

Classical/ logical method

Answer 5

using basic knowledge like flipping a coin

Question 6

Subjective Probability

Answer 6

No logic or past knowledge available

Opinion polls

Question 7

Mutually exclusive

Answer 7

only one of the events can occur on any one trial

Question 8

Collectively exhaustive

Answer 8

the list of outcomes include every possible outcome

Question 9

P( A U B) =

Answer 9

P(A) +P(B) - P(A + B)

Question 10

Two events are independent if

Answer 10

P(A and B) = P(A) * P(B)
P(AIB) = P(A)
They have no impact on one another

Question 11

Conditional Probability

Answer 11

Event occurs given another event already occurs

Question 12

P(BIA) =

Answer 12

P(A and B) / P (A)

divided by what it depends on

Question 13

Bayes Theorem

Answer 13

Used to incorporate additional information and help create posterior possibilities from original or prior probabilities
Prior possibilities + new info –> bayes process–> posterior prob

Question 14

Bayes theorem equation

Answer 14

P(A I B) = P( BIA) * P(A) / P(BIA)* P(A) + P(B I A’) * P(A’)
multiply by what is after I

Question 15

Random Variable

Answer 15

Assigns a real number to every possible event or outcome

Question 16

Two types of RV

Answer 16

Discrete: finite set of values
Continuous: Infinite set of values

Question 17

Expected Value

Answer 17

Central tendency of the distribution. compute as the weighted average of the values of the random variable

Question 18

Finding expected value of a discrete prob distribution

Answer 18

multiply each possible value of RV, Xi, by the probability that outcome will occur, P(Xi), and adding them all together

Question 19

Variance of a discrete prob distribution

Answer 19

each value of the Rv is subtracted from the expected value, squared, and * the prob of occurence.

Question 20

binomial

Answer 20

find the prob of a specific # of successes out of n trials

Question 21

Binomial equation

Answer 21

(n!/ r! (n-r)!) * p^r * q ^n-r

n= trials. p = prob of success in 1 trial. r= # of successes q=1-p

Question 22

Empiral rule

Answer 22

68% of values are plus or minus 1 st dev from mean
about 95% of values are plus or minus 1 st dev from mean
about 99.7% of values are plus or minus 1 st dev from mean

Question 23

Poisson dist

Answer 23

involves rate (llamda) 
= llamda e ^- llamda/ x!
llamda = mean rate 
e= 2.718
x= # of occurences