Suppose That the Amount of Water, in Thousands of Gallons $$F ( x ) = \left\{ \begin{array} { l l } 1 - \frac { 1 } { e ^ { x } } & x \geq 0 \\0 & \text { elsewhere }\end{array} \right.$$

Essay

Suppose that the amount of water, in thousands of gallons, which fall on a city during a rain storm has distribution function: $$F ( x ) = \left\{ \begin{array} { l l } 1 - \frac { 1 } { e ^ { x } } & x \geq 0 \\0 & \text { elsewhere }\end{array} \right.$$ Find the probability that, in a rain storm, at least 2000 gallons of water fall, given that 1200 gallons have already fallen. Is this different than the probability that 800 gallons fall without any prior knowledge?