The time interval between the arrivals of successive trains at a certain station is measured by a random variable X with a probability density function $$f ( x ) = \left\{ \begin{array} { l l }
0.4 e ^ { - 0.4 x } & \text { for } x \geq 0 \
0 & \text { for } x

Question

The time interval between the arrivals of successive trains at a certain station is measured by a random variable X with a probability density function $$f ( x ) = \left\{ \begin{array} { l l } 
0.4 e ^ { - 0.4 x } & \text { for } x \geq 0 \
0 & \text { for } x < 0
\end{array} \right.$$ where x is the time (in minutes) between the arrivals of a randomly selected pair of successive trains. What is the probability that two successive trains selected at random will arrive within 2 minutes of one another? Round to the nearest hundredth.

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The Answer of The time interval between the arrivals of successive trains at a certain station is measured by a random variable X with a probability density function $$f ( x ) = \left\{ \begin{array} { l l } 
0.4 e ^ { - 0.4 x } & \text { for } x \geq 0 \
0 & \text { for } x < 0
\end{array} \right.$$ where x is the time (in minutes) between the arrivals of a randomly selected pair of successive trains. What is the probability that two successive trains selected at random will arrive within 2 minutes of one another? Round to the nearest hundredth.

The Time Interval Between the Arrivals of Successive Trains at a Certain