Probability theory and random variables

Question 1

sample space

Answer 1

of a random experiment= set S of all possible outcomes

Question 2

elementary outcome

Answer 2

• Each single outcome (how many results)

Question 3

event

Answer 3

set of one or more elementary outcome for a random experiment
o E.g. when you take every dot higher than 4 on a dice you get 3 (4 5 6)

Question 4

Disjoint

Answer 4

when two or more events have no EO s in common (if P(A and B) and P(A|B) are 0)

Question 5

Probability model

Answer 5

probabilities are assigned to events

Question 6

probability

Answer 6

of an event A in a random experiment P(A)

Question 7

Relative frequency

Answer 7

how often does a special event occurs if you keep doing the experiment for a large (not limited number)

Question 8

Unconditional probability P(F)

Answer 8

the probability that the random drawn student is female

Question 9

Conditional probability (F|D)

Answer 9

probability of the randomly drawn student being female, given that the student is Dutch (the given one is always the total you divide by

Question 10

Complement rule

Answer 10

G^c = event “the randomly drawn student is not german” 1-P(A)

Question 11

Rule of addition

Answer 11

What is the probability of randomly drawn student is dutch or Belgian
P(A or B) = P(A) + P(B) - P(A and B)

Question 12

rule of multiplication

Answer 12

Probability of randomly drawn student being dutch and female P (D and F)
P(A and B) = P(A) × P(B | A) = P(B) × P(A | B)

Question 13

Statistical independent

Answer 13

P(A|B) = P(B)

Question 14

Probability distribution

Answer 14

relative freq. of each of the possible values of X if you were to repeat random experiment an infinite number of times

Question 15

P(A)

Answer 15

number of A divided by the total

Question 16

P(A|B)

Answer 16

number of A within subset B divided by number of B

Question 17

P(A and B)

Answer 17

number of (A and B) divided by the total
o	When you have no contingency table you can use product rule: P(A) * P(B|A)

Question 18

P(A or B)

Answer 18

use additional rule: P(A) + P(B) – P(A and B)