probability

Question 1

U

Answer 1

union

Question 2

∩

Answer 2

intersection

Question 3

∅

Answer 3

empty set

Question 4

−

Answer 4

difference

Question 5

⊆, ⊂

Answer 5

subset

Question 6

∈, ∉

Answer 6

contains

Question 7

| |

|

Answer 7

number of elements

Question 8

[ ], ( )

Answer 8

set limits

Question 9

∀

Answer 9

for all

Question 10

probability

Answer 10

A number between 0 and 1, describing the relative possibility (chance of likelihood) that an event will occur

Question 11

small probability

Answer 11

unlikely

Question 12

high probability

Answer 12

likely

Question 13

A random variable X

Answer 13

a variable which can take a value out of a set of values, due to chance, unobserved factors or measurement errors

Question 14

Probability P

Answer 14

the chance or likelihood that we observe something

Question 15

sample space S

Answer 15

the set of all possible outcomes

Question 16

event E ⊆ S

Answer 16

a collection of one or more outcomes

Question 17

possible outcome x ∈ S

Answer 17

one of the values that X can take

Question 18

union of events: A U B

Answer 18

all possible outcomes in A or in B

Question 19

intersection of events: A n B

Answer 19

all possible outcomes in A and in B

Question 20

difference of events: A – B

Answer 20

all possible outcomes in A that are not in B

Question 21

complementary event A’ = S – A

Answer 21

All possible outcomes that are not in A

Question 22

probability of an event

Answer 22

number of favourable outcomes divided by the number of possible outcomes

Question 23

categorical variable

Answer 23

random variable that represents a quality or category

Question 24

numerical variable

Answer 24

a random variable that can be measured.

Question 25

dichotomous or binary variable

Answer 25

it can only take two variables (yes or no)

Question 26

nominal variable

Answer 26

there is no order and it is mutually exclusive (A-B-C)

Question 27

ordinal variable

Answer 27

it can be ordered and it is mutually exclusive and “Quasi-quantitative” (I-II-III)

Question 28

discrete variable

Answer 28

the sample space is countable, there is a finite number of values (2-4-6)

Question 29

continuous variable

Answer 29

the sample space is uncountable, between a min and max value (2,3-3,5-4,6)

Question 30

conditional probability

Answer 30

the probability of A, given that B happened

Question 31

Bayes theorem

Answer 31

P(A|B) = P(A n B)/P(B)

Question 32

two interdependent events A, B ⊆ S

Answer 32

P(A n B) = P(A)P(B)

Question 33

uniform distribution (discrete)

Answer 33

all values have the same probability (eg dice)

Question 34

bernouilli distribution (discrete)

Answer 34

binary variables. Success and Failure

Question 35

Binomial distribution (discrete)

Answer 35

the number of successes in n Bernouilli runs with probability p

Question 36

poisson distribution (discrete)

Answer 36

• k ∈ {0,1,2,…} is the number of times an event occurs in an interval
• events are independent
• the average rate at which events occur is independent if any occurences
• two events cannot occure at exactly the same instant

Question 37

uniform distribution (continuous)

Answer 37

The outcomes are equally likely

Question 38

normal (gaussian) distribution (continuous)

Answer 38

it is symmetric at the mean, showing that the data close to the mean is more frequent than far from from the mean

Question 39

central limit theorem

Answer 39

in some situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution.

Question 40

beta distribution (continuous)

Answer 40

this is often used to model the uncertainty about the probability of success of an experiment

Question 41

chi-square ditribution (continuous)

Answer 41

it is a distribution with k degrees of freedom. It is used to describe the distribution of a sum of squared random variables.

Question 42

lognormal distribution

Answer 42

eg the income of 97%-99% of the population, city sizes

Question 43

pareto distribution (80-20 rule)

Answer 43

eg income, sizes of human settlements, values of oil reserves in oil fields, standardized price returns on individual stocks

Question 44

negative binomial distribution

Answer 44

number of failures before a given number of successes in a binomial

Question 45

exponential distribution

Answer 45

time between two consecutive next Poisson-type events

Question 46

gamma distribution

Answer 46

time before the next k Poisson-type events occur