Lecture #16 - Random Processes

Question 1

What is a random variable?

Answer 1

A random variable is a function that assigns a real number to each outcome in the sample space of a random experiment.

Question 2

What is covariance?

Answer 2

The measure of how two random variables change together

Question 3

What’s a random process

Answer 3

A collection of random variables, characterised by a set of probability distribution functions that are a function of time.

Question 4

When would you use a random process?

Answer 4

Modelling any natural phenomena

Question 5

What is the difference between a random variable and a random process w.r.t the output of an experiment?

Answer 5

RV, the output is mapped to a number

RP, the output of the experiment is mapped to a waveform which is a function of time.

Question 6

What does it mean for a random process X(t) to be strictly stationary

Answer 6

If the joint probability distribution is time-invariant

Question 7

Explain the relationship between strict sense stationary process and wide sense stationary

Answer 7

Strict sense stationary process is always wide sense stationary, but not the other way around.

Question 8

Describe what a cyclostationary process is

Answer 8

1. Signal whose statistical properties vary cyclically with time

PAM

Question 9

Describe what a locally stationary or quasi-stationary is

Answer 9

• Statistical properties change slowly over short periods of time.
• Globally nonstationary, but approximately locally stationary, and are
• Modelled as if the statistics actually are stationary over a short segments
• E.g. speech

Question 10

What does a stationary process mean?

Answer 10

If the statistical properties do not change over time.