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

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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) ={0.2e0.2x for x00 for x<0f ( 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.

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Definitions:

Psychoactive Drug

A chemical substance that changes brain function and results in alterations in perception, mood, consciousness, cognition, or behavior.

Visual Hallucinations

Perceptual experiences during which individuals see objects or events that have no reality or external source in the presence of a waking state.

LSD

Lysergic acid diethylamide, a psychedelic drug known for its psychological effects, which may include altered awareness of surroundings, perceptions, and feelings as well as sensations and images that seem real though they are not.

Social Anxiety Disorder

A mental health disorder characterized by significant and persistent fear of social situations due to perceived scrutiny by others, leading to avoidance of such situations.

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