Week 4 (Probability theory)

Question 1

What is the definition of an experiment in probability theory?

Answer 1

an activity which produces or observes an outcome

Question 2

What is sample space in probability?

Answer 2

a set of possible outcomes in curly brackets

Question 3

What is an event in probability theory?

Answer 3

a subset of the sample space, so one or more possible outcomes from the sample space

elementary events consist of one possible outcome

Question 4

What is N in probability?

Answer 4

the number of independent events in the sample space

Question 5

what is X in probability?

Answer 5

a random variable which denotes which of the independent events has occured

Question 6

what is the law of large numbers?

Answer 6

as the sample size increases, the observed probability approaches the true underlying probability

Question 7

what are the formal features of probability?

Answer 7

• the probability of an event cannot be negative
• the probability of each event in the sample space must add up to 1
• The probability of any individual event cannot be greater than 1

Question 8

how would we calculate the possibility of either one of two events occuring

Answer 8

• we would add together the individual probaility of each event occuring
• we would then subtract the possibility that both events occur together

Question 9

what is a probability distribution

Answer 9

the probability of all possible outcomes in an experiment

Question 10

what is a binomial distribution?

Answer 10

a probability distribution where you have two possible outcomes

Question 11

what is a cumulative distribution?

Answer 11

a distribution of the probability that a random variable x is equal to or less than x

Question 12

How would you write that the probability of A is not conditional on the probability of B?

Answer 12

P(A | B) = P(A)

Question 13

What do the terms in the binomial distribution stand for?

Answer 13

b= binomial probability
x= total number of successes
p= probability of successes in any given trial
n= number of trials

Question 14

how do you write the conditional probability of A given B?

Answer 14

P(A|B)

Question 15

what is the difference between conditional probability and joint probability?

Answer 15

Joint probability is the probability of A and B occuring at the same time

Conditional probability is the probability of B occuring, given the knowledge that event A has already occured

Question 16

how do you write the joint probability

Answer 16

With an upside down U

Question 17

how would you compute the conditional probability of A given B

Answer 17

P(A|B) = Joint probability of A&B / Overall probability of B

Question 18

What is statistical independence between two variables and how can you express it?

Answer 18

independence means that the value of one variable doesnt tell us anything about the value of the other

This can be expressed as P(A|B) = P(A)