Lecture 3

Question 1

experiment

Answer 1

set of rules that governs a specific procedure, which can be indefinitely repeated and has well-defined set of outcomes

deterministic / random

Question 2

deterministic experiment

Answer 2

has only one possible outcome

Question 3

random experiment

Answer 3

has two or more possible outcomes

Question 4

trial

Answer 4

performance or exercise of a defined experiment

Question 5

outcome

Answer 5

result of a given trail

Question 6

sample space

Answer 6

set of all possible outcomes of an experiment

omega

Question 7

uniform probability distribution

Answer 7

every outcome has the same probability

Question 8

Kolmogorov’s axioms

Answer 8

1. probability of an event is non-negative number
2. probability that some elementary event in the entire sample space will occur is 1
3. any countable sequence of disjoint events satisfies that union of the probabilities is their sum

Question 9

stochastic variable

Answer 9

function X mapping the probability space of a random experiment to real numbers

Question 10

measurement noise

Answer 10

example of stochastic variable

any variation in the measured signal that obscures the theoretical true wave you are trying to achieve

Question 11

ergodicity

Answer 11

process that behaves the same whether analysed over time or averaged over space

Question 12

non-ergodicity

Answer 12

when the underlying physical process changes its characteristics

Question 13

realization

Answer 13

actually observed outcome of the process

Question 14

probability distribution

Answer 14

describes the probability of a stochastic variable taking certain values

Question 15

cumulative distribution

Answer 15

probability that a stochastic variable will be found at a value less than or equal to x

Question 16

statistical moments

Answer 16

quantitative measure of the shape of a set of points

k-th moment, central moment, standarized moment