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?

Question

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?

Quizplus · Accepted Answer

The Answer of 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?

Suppose That the Amount of Water, in Thousands of Gallons F(x)={1−1exx≥00 elsewhere F ( x ) = \left\{ \begin{array} { l l } 1 - \frac { 1 } { e ^ { x } } & x \geq 0 \\0 & \text { elsewhere }\end{array} \right.F(x)={1−ex1​0​x≥0 elsewhere ​

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