a. To determine Find the probability that there are no counts in a 30-second interval. Explanation Given info: The Geiger counter counts follow Poisson distribution with an average of two counts per minute. Calculation: The random variable X follows the exponential distribution with parameter λ . Then the probability density function is, f ( x ) = λ e − λ x for x > 0 Let the random variable X denotes the counts recorded by a Geiger counter. The probability density function is, f ( x ) = 2 e − 2 x for 0 < x Covert the seconds into minutes, because the mean value indicates in minutes. 60 seconds = 1 minute 30 seconds = 0.5 minutes Calculate the probability for the no count occurs in 30 seconds is P ( X > 0 b. To determine Find the probability that the first count happens in less than 10 seconds. c. To determine Find the probability for the first count happens between the one and two minutes after start-up.

Applied Statistics and Probability for Engineers

6th Edition

ISBN: 9781118539712

Author: Douglas C. Montgomery

Publisher: WILEY

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Chapter 4.8, Problem 115E

To determine

Find the probability that there are no counts in a 30-second interval.

To determine

Find the probability that the first count happens in less than 10 seconds.

To determine

Find the probability for the first count happens between the one and two minutes after start-up.

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Chapter 4.8, Problem 114E

Chapter 4.8, Problem 116E

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Applied Statistics and Probability for Engineers

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