Week 2

Question 1

Probability

Answer 1

A measure of the likelihood that an event occurs, on a scale from 0 to 1.

Question 2

If B1, B2, B3, …, Bn is a part of event B, then P(B) = :

Answer 2

P(B) = P(B1) + P(B2) + P(B3) + … + P(Bn)

Question 3

What does the addition rule say?
(probability)

Answer 3

If something can happen in different ways, the probability that it happens is the sum of the probabilities of all the different ways it can happen.

Question 4

indicator

Answer 4

The outcome of a certain event

Question 5

Unifrom distribution

Answer 5

Equal probability for all events in the set.

Question 6

Uniform (a,b) distribution

Answer 6

When a point is picked randomly from the interval (a,b) with equal probabilities for all points. a<b

Question 7

What is the probability that a point falls within a certain interval (x,y) with a<x<y<b when there is a uniform (a,b) distribution?

Answer 7

(y-x) / (b-a)

Question 8

Give a formula using only unconditional probabilities for P(A|B) :

Answer 8

P(AB) / P(B)

Question 9

When are two events A and B called independent?

Answer 9

When P(A|B) = P(A).

Question 10

For two events A and B, P(AB) is equal to…

Answer 10

P(A) * P(B)

Question 11

Finish the Bayes’ rule:
For a partition B1, B2, … Bn of all possible outcomes, P(Bi|A) =

Answer 11

P(A|Bi) * P(Bi)
—————————————————-/
P(A|B1)P(B1) + … + P(A|Bn)P(Bn)

Question 12

Each path through the tree represents a sequence of possible outcomes for the various stages. What do you do to find the probability of a path?

Answer 12

Multiply the conditional probabilities along the branches.
e.g. P(1) * P(2|1) * P(3|2)…

Question 13

Each path through the tree represents a sequence of possible outcomes for the various stages. What do you do to find the probability of an event?

Answer 13

Identify the corresponding set of paths and sum the probabilities of these paths.

Question 14

What is the formula for (N/X) in the formula for P(X) with replacement?

Answer 14

(N/X) = N! / (X! * (N-X))

Question 15

Binomial distribution

Answer 15

with replacement

Question 16

What is the probability P(X) of a certain amount X of red marbles in the vase in the marbles-vase model WITH replacement?

Answer 16

P(X) = (N/X) * mu^X * ( (1-mu)^(N-X) )

The amount of marbles in the vase divided by X times the proportion of red marbles to the X-th, times the proportion of green marbles to the amount of green marbles in the vase (N-X).

Question 17

In KNN, what is the training time?

Answer 17

O(1), it is constant.

Question 18

What is a prerequisite for matrix multiplication?

Answer 18

A of dimensions a x b and B of dimensions c x d can only be multiplied if b=c.

Question 19

In KNN, what is the test time?

Answer 19

O(n), it depends on the number of test examples.