average number

[logistic_guy]

The probability distribution of \(\displaystyle X\), the number of imperfections per \(\displaystyle 10\) meters of a synthetic fabric in continuous rolls of uniform width, is given as

\(\displaystyle x\)​	\(\displaystyle 0\)​	\(\displaystyle 1\)​	\(\displaystyle 2\)​	\(\displaystyle 3\)​	\(\displaystyle 4\)​
\(\displaystyle f(x)\)​	\(\displaystyle 0.41\)​	\(\displaystyle 0.37\)​	\(\displaystyle 0.16\)​	\(\displaystyle 0.05\)​	\(\displaystyle 0.01\)​

Find the average number of imperfections per \(\displaystyle 10\) meters of this fabric.

 

[logistic_guy]

The average value is the same as the expectation, so:

\(\displaystyle \text{average number} = E(x) = \sum_{x=0}^{4}xf(x)\)

Or

\(\displaystyle E(x) = 0(0.41) + 1(0.37) + 2(0.16) + 3(0.05) + 4(0.01) = \textcolor{blue}{0.88}\)