Poisson Distribution Problem: Missing Pulses in a Computer Disk

Math Problem Statement

Consider writing onto a computer disk and then sending it through a certifier that counts the number of missing pulses. Suppose this number X has a Poisson distribution with parameter 𝜇 =0.5. (Round your answers to three decimal places.)

(a) What is the probability that a disk has exactly one missing pulse?

(b) What is the probability that a disk has at least two missing pulses?

Solution

We are given that the number $X$ of missing pulses follows a Poisson distribution with parameter $\mu = 0.5$ . The probability mass function (PMF) of a Poisson distribution is given by:

$P(X = k) = \frac{e^{-\mu} \mu^k}{k!}$ where $k$ is the number of missing pulses and $\mu = 0.5$ .

Part (a): Probability that a disk has exactly one missing pulse

We need to find $P(X = 1)$ . Using the Poisson PMF formula:

[ P(X = 1) =

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Math Problem Analysis

Mathematical Concepts

Poisson Distribution
Probability Theory

Formulas

Poisson PMF: P(X = k) = (e^(-𝜇) * 𝜇^k) / k!

Theorems

Poisson Theorem
Probability of Independent Events

Suitable Grade Level

Undergraduate Statistics

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