Probability of No Particle Detections for 2.8 Minutes With Exponential Distribution

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The document describes an experiment using a geiger counter to detect particles. The time between detections (X) has an exponential distribution with a mean of 1.4 minutes. It asks to find the probability that no particles are detected over a period of 2.8 minutes from starting the counter.

Formation

Let X denote the time between detections of a particle with a geiger counter and assume that X
has an exponential distribution with mean 1.4 minutes. Find the probability that no particles are
detected for 2.8 minutes of starting the counter.
Solution
r = 1/1.4
= rt = 1/1.4(2.8) = 2
P(X = 0) = e- = e-2 = 0.135335283236613

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