The number of electrical outages in a city varies from day to day.Assume that the number of electrical outages (x) in the city has the following probability distribution.
$$\begin{array} { c c }
x & f ( x ) \
\hline 0 & 0.80 \
1 & 0.15 \
2 & 0.04 \
3 & 0.01
\end{array}$$
The mean and the standard deviation for the number of electrical outages (respectively) are

A) 2.6 and 5.77
B) 0.26 and 0.577
C) 3 and 0.01
D) 0 and 0.8

Question

The number of electrical outages in a city varies from day to day.Assume that the number of electrical outages (x) in the city has the following probability distribution. 
$$\begin{array} { c c } 
x & f ( x ) \
\hline 0 & 0.80 \
1 & 0.15 \
2 & 0.04 \
3 & 0.01
\end{array}$$  
The mean and the standard deviation for the number of electrical outages (respectively) are
 
A)  2.6 and 5.77
B)  0.26 and 0.577
C)  3 and 0.01
D)  0 and 0.8

Quizplus · Accepted Answer

The mean is calculated as $ \sum x \cdot f(x) = 0 \cdot 0.80 + 1 \cdot 0.15 + 2 \cdot 0.04 + 3 \cdot 0.01 = 0.26 $. The variance is $ \sum (x - \text{mean})^2 \cdot f(x) = 0.5776 $, so the standard deviation is $ \sqrt{0.5776} \approx 0.577 $.

The Number of Electrical Outages in a City Varies from Day