expectation example
The contraharmonic mean of several positive numbers ${u}_{1}$, ${u}_{2}$, $\mathrm{\dots}$, ${u}_{n}$ is defined as
$$c:=\frac{{u}_{1}^{2}+{u}_{2}^{2}+\mathrm{\dots}+{u}_{n}^{2}}{{u}_{1}+{u}_{2}+\mathrm{\dots}+{u}_{n}}.$$ |
This has certain applications; one of them is by [1] the following.
If $\u27e8{u}_{1}$, ${u}_{2}$, $\mathrm{\dots}$, ${u}_{n}\u27e9$ is the distribution^{} of the seats of $n$ parties, $s$ the total number of seats in the body of delegates (${u}_{1}+{u}_{2}+\mathrm{\dots}+{u}_{n}=s$), and one draws a random seat (with probability $1/s$), then the size of the drawn delegate’s party has the expected value
$$\frac{{u}_{1}}{s}\cdot {u}_{1}+\frac{{u}_{2}}{s}\cdot {u}_{2}+\mathrm{\dots}+\frac{{u}_{n}}{s}\cdot {u}_{n}=c.$$ |
References
- 1 Caulier, Jean-François: The interpretation^{} of the Laakso–Taagepera effective number of parties. – Documents de travail du Centre d’Economie de la Sorbonne (2011.06).
Title | expectation example |
---|---|
Canonical name | ExpectationExample |
Date of creation | 2013-11-05 17:59:13 |
Last modified on | 2013-11-05 17:59:13 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 2 |
Author | pahio (2872) |
Entry type | Example |
Classification | msc 05A18 |
Classification | msc 26E60 |
Classification | msc 60A05 |