Revision as of 16:14, 20 April 2002 edit Miguel~enwiki (talk \| contribs) 3,710 edits m *functions of random variables are random variables. Example of cdf of X^2. Links to random vector and random function ← Previous edit		Revision as of 05:44, 25 April 2002 edit undo Miguel~enwiki (talk \| contribs) 3,710 edits m *removed redundancies. Added generating function Next edit →
Line 19: :F<sub>''Y''</sub>(''y'')=Prob(''f''(''X'')≤y). ==== Example: ==== Let ''f''(''x'')=''x''<sup>2</sup>. Then, :F<sub>''Y''</sub>(''y'')=Prob(''X''<sup>2</sup>≤y). Line 30 ⟶ 32: === Moments === A random variable can often be characterised by a small number of quantities, which also have a practical interpretation. For example, it is often enough to know what its "average value" is. ~~For instance, what is the average of the results you get when you roll a die represtedly, or measure human heights?~~ This is captured by the mathematical concept of [[expected value]] of a random variable, denoted E[''X'']. Once the "average value" is known, one could then ask "how far are the values of ''X'' typically away from the average", a question that is answered by the [[variance]] and [[standard deviation]] of a random variable. Mathematically, this is known as the (generalised) [[problem of moments]]: for a given class of random variables ''X'', find a collection {''f<sub>i</sub>''} of functions such that the expectation values E[''f<sub>i</sub>''(''X'')] fully characterize the distribution of the random variable ''X''. See also: [[discrete random variable]], [[continuous random variable]], [[probability distribution]], [[random vector]], [[random function]], [[generating function]]

Random variable: Difference between revisions