This video discusses why it is useful to characterise a probability
density function (pdf) in terms of salient features which measure the
location, spread, asymmetry, and the tails of the density. Other key
statistics are also mentioned in relation to this characterisation. The
expected value is then formally introduced both for continuous random
variables, but also for discrete random variables. The properties of the
mean value is then considered for even and symmetric densities. Next,
the video looks at the invariance of the expectation operator for
finding the expected value of a nonlinear function of another random
variable, including a proof. The video finishes with an example showing
the expected value of a trigonometric transformation of a uniform random
PGEE11164 Probability, Estimation Theory, and Random Signals Lectures -- School of Engineering, University of Edinburgh. Copyright James R. Hopgood and University of Edinburgh, Scotland, United Kingdom (UK). 2020.
Institute for Digital Communications, Alexander Graham Bell Building, The King's Buildings, Thomas Bayes Road, Edinburgh, EH9 3JL. UK.