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

question 15

Multiple Choice

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 $f ( x ) = \left\{ \begin{array} { l l } 0.2 e ^ { - 0.2 x } & \text { for } x \geq 0 \\0 & \text { for } x < 0\end{array} \right.$ 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 9 minutes of one another? Round to the nearest hundredth.

• A)0.17
• B)0.83
• C)0.62
• D)0.42

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