Chapter 6, Problem T6.3SPT

To determine

To compute:The standard deviation of D.

Answer to Problem T6.3SPT

The standard deviation of D is 0.9.

Explanation of Solution

Given:

The probability distribution is:

x	1	2	3	4
P(x)	0.20	0.40	0.30	0.10

Calculation:

The standard deviation of D, can be calculate as:

  $\begin{array}{c}E\left(x\right)={\displaystyle \sum xp\left(x\right)}\\ =1\left(0.2\right)+2\left(0.4\right)+3\left(0.3\right)+4\left(0.1\right)\\ =0.2+0.8+0.9+0.4\\ =2.3\\ V\left(X\right)=E{\left(X-E\left(X\right)\right)}^2\\ =E{\left(X-2.3\right)}^2\\ ={\displaystyle \sum {\left(x-2.3\right)}^{2}p\left(x\right)}\\ ={\left(1-2.3\right)}^{2}p\left(1\right)+{\left(2-2.3\right)}^{2}p\left(2\right)+{\left(3-2.3\right)}^{2}p\left(3\right)+{\left(4-2.3\right)}^{2}p\left(4\right)\\ =0.338+0.036+0.147+0.289\\ =0.81\\ SD=\sqrt{V\left(X\right)}\\ =\sqrt{0.81}\\ =0.9\end{array}$

Thus, the correct option is 0.9.