Freeflows

Weighted Die Expected Value

A 6-sided die is weighted so that the probability of any number being rolled is proportional to the value of the roll. (So, for example, the probability of a 2 being rolled is twice that of a 1 being rolled.) What is the expected value of a roll of this weighted die? Express your answer as a common fraction.

1
2
3
+
4
5
6
-
7
8
9
$\frac{a}{b}$
.
0
=
%

$a^n$
$a^{\circ}$
$a_n$
$\sqrt{}$
$\sqrt[n]{}$
$\pi$
$\ln{}$
$\log$
$\theta$
$\sin{}$
$\cos{}$
$\tan{}$

$($
$)$
$[$
$]$
$\cap$
$\cup$
$,$
$\infty$

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