The probability density function of evaporation $$E$$ on any day during a year in a watershed is given by $$$f\left( E \right) = \left\{ {\matrix{ {{1 \over 5}} & {0 \le E \le 5\,mm/day} \cr 0 & {otherwise} \cr } } \right.$$$
The probability that $$E$$ lies in between $$2$$ and $$4$$ $$mm/day$$ in the watershed is (in decimal) _______.

A traffic office imposes on an average $$5$$ number of penalties daily on traffic violators. Assume that the number of penalties on different days is independent and follows a Poisson distribution. The probability that there will be less than $$4$$ penalties in a day is ________.

A straight 100 m long raw water gravity main is to carry water from an intake structure to the jack well of a water treatment plant. The required flow through this water main is 0.21 $$m^3/s$$. Allowable velocity through the main is 0.75 m/s. Assume f = 0.01, g = 9.81 $$m/s^2$$. The minimum gradient (in cm/100m length) to be given to this gravity main so that the required amount of water flows without any difficulty is _____.

Some of the nontoxic metals normally found in natural water are