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7. A light sensor uses a photodetector whose output is modeled as a Poisson random variable X, with mean A. The sensor triggers an alarm if X> 15. If λ=10, find the probability that the alarm is triggered.

7. A light sensor uses a photodetector whose output is modeled as a Poisson random variable X, with mean A. The sensor triggers an alarm if X> 15. If λ=10, find the probability that the alarm is triggered.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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7. Help please
**Problem Statement:** A light sensor uses a photodetector whose output is modeled as a Poisson random variable \(X\), with mean \(\lambda\). The sensor triggers an alarm if \(X > 15\). If \(\lambda = 10\), find the probability that the alarm is triggered. **Explanation:** To solve this problem, you'll need to use the properties of the Poisson distribution. The Poisson probability mass function is given by: \[ P(X = k) = \frac{e^{-\lambda} \lambda^k}{k!} \] where \(\lambda = 10\) and \(k\) is the number of occurrences. However, we need the probability that \(X > 15\), which is: \[ P(X > 15) = 1 - P(X \leq 15) \] This calculation involves determining the cumulative probability from \(X = 0\) to \(X = 15\) and subtracting it from 1 to find our desired probability.
Transcribed Image Text:**Problem Statement:** A light sensor uses a photodetector whose output is modeled as a Poisson random variable \(X\), with mean \(\lambda\). The sensor triggers an alarm if \(X > 15\). If \(\lambda = 10\), find the probability that the alarm is triggered. **Explanation:** To solve this problem, you'll need to use the properties of the Poisson distribution. The Poisson probability mass function is given by: \[ P(X = k) = \frac{e^{-\lambda} \lambda^k}{k!} \] where \(\lambda = 10\) and \(k\) is the number of occurrences. However, we need the probability that \(X > 15\), which is: \[ P(X > 15) = 1 - P(X \leq 15) \] This calculation involves determining the cumulative probability from \(X = 0\) to \(X = 15\) and subtracting it from 1 to find our desired probability.
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Step 1: Given information

The provided information is as follows:
The X tilde P left parenthesis lambda right parenthesis.
lambda equals 10.
The sensor triggers the alarm if X greater than 15.

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