Chapter 1 : Probability recap

Question 1

Conditional probability in terms of joint and marginal

Answer 1

Joint probability over the marginal probability

Question 2

Partition

Answer 2

Means events are disjoint (intersection of 0) and the union of sets is the full sample space

Question 3

Prior probability

Answer 3

a probability as assessed before making reference to certain relevant observations

Question 4

Posterior probability

Answer 4

Our prior is updated after having observed the data

Question 5

What is the rule for sequential calculations using bayes rule

Answer 5

Old posterior becomes he new prior

Question 6

Define a random variable

Answer 6

function from a sample space into a real number

Question 7

what is the standard deviation

Answer 7

square root of the variance

Question 8

Explain equi dispersed and give an example of a distribution that it

Answer 8

Meaning expectation equals variance - poisson distribution

Question 9

What is the relation between a continuous pdf and cdf

Answer 9

a probability density function (pdf) is the derivative of a cumulative distribution function (cdf)

Question 10

What are the parameters of a normal distirbution

Answer 10

mean and the standard deviation (sigma)

Question 11

Define the mode

Answer 11

The most probable value of an RV

Question 12

Define the median

Answer 12

The value of the RV in the middle of the distribution

Question 13

Define the expected value

Answer 13

A one number summary of the central location of the RV

Question 14

What does linearity of expectation mean

Answer 14

expectation of the sum = sum of the expectations

Question 15

Explain variance

Answer 15

average squared distance a sample value is from the expected value

Question 16

What si the joint distirbution in terms of the marginal and conditional

Answer 16

Marginal x conditional

Question 17

How do I know if RVs are independent based on their joint density

Answer 17

If joint = product of marginal they are conditionally independent