Let $x$ be a variable assuming values $1,2,\ldots,k$ and let $F(1)=n,\ldots,F(n)$ be the corresponding cumulative frequencies of the 'greater than' type. Show that
$$\text{Mean of }x=\frac{ F(1)+\cdots+F(k) }n.$$
Asked
Active
Viewed 26 times
1 Answers
0
Note $$\begin{align}\sum_x x P[X=x] &= 1\cdot P[X=1]+2\cdot P[X=2]+\cdots +k\cdot P[X=k]\\&=(P[X=1]+P[X=2]+\cdots +P[X=k]) \\&+(P[X=2]+\cdots +P[X=k])\\ & \vdots\\&+P[X=k]\\ &= F(1)+F(2)+\cdots+F(k)\end{align}$$
Argha
- 4,671
-
i said mean. not expectation of x – soumajit das Oct 28 '14 at 16:49
-
@soumajitdas: Just replace $P[X=x]$ by $\dfrac{f_x}{n}$. You get your desire answer.. – Argha Oct 28 '14 at 16:58