Question

The probability density function of evaporation E on any day during a year in watershed is given by $f\left(E\right)=(\begin{array}{cc}\frac{1}{5}& 0\le E\le 5\mathrm{mm}/\mathrm{day}\\ 0& \mathrm{otherwise}\end{array}$
The probability that E lies in between 2 and 4 mm/day in a day in watershed is (in decimal)

• A. 0.4

Answer 1

The correct option is A 0.4

$f\left(x\right)=\{\begin{array}{cc}\frac{1}{5}& 0\le E\le 5\text{mm/day}\\ 0& \text{otherwise}\end{array}$
$P(2<E<4)={\int }_2^{4}f\left(E\right)\mathrm{dE}={\int }_2^4\frac{1}{5}\mathrm{dE}=\frac{1}{5}{\left(E\right]}_2^4$

$=\frac{1}{5}(4-2)=2/5$