/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 40 Let \(x\) be a Poisson random va... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 40

Let \(x\) be a Poisson random variable with mean \(\mu=2.5 .\) Use Table 2 in Appendix I to calculate these probabilities: a. \(P(x \geq 5)\) b. \(P(x<6)\) c. \(P(x=2)\) d. \(P(1 \leq x \leq 4)\)

Short Answer

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Question: Given a Poisson random variable \(x\) with mean \(\mu = 2.5\), calculate the following probabilities: \(P(x \geq 5)\), \(P(x<6)\), \(P(x=2)\), and \(P(1 \leq x \leq 4)\). Solution: 1. To find \(P(x \geq 5)\), first calculate the complement probability \(P(x < 5)\) by adding the probabilities for \(x=0, 1, 2, 3,\) and \(4\) from Table 2 for the mean 2.5 . Then use the formula \(P(x \geq 5) = 1 - P(x < 5)\) to find the final probability. 2. To find \(P(x<6)\), add the probabilities for \(x=0, 1, 2, 3, 4,\) and \(5\) from Table 2 for the mean 2.5. 3. To find \(P(x=2)\), directly get the corresponding probability from Table 2 for the mean 2.5 and \(x=2\). 4. To find \(P(1 \leq x \leq 4)\), add the probabilities for \(x=1, 2, 3,\) and \(4\) from Table 2 for the mean 2.5.

Step by step solution

01

Find the probabilities using Table 2

Using Table 2 in Appendix I, we can look for the probabilities \(P(x=k)\) for each value of \(k\) given the mean \(\mu=2.5\). We will need these values to compute the requested probabilities.
02

Compute the probability that \(P(x \geq 5)\)

To find \(P(x \geq 5)\), we need to find the complement probability \(P(x < 5)\), which is the sum of the probabilities for \(x=0\), \(x=1\), \(x=2\), \(x=3\), and \(x=4\). Then we can find \(P(x \geq 5)\) by using the formula \(P(x \geq 5) = 1 - P(x < 5)\). Add the corresponding probabilities for each value of \(x\) from Table 2 and then subtract the sum from 1 to find \(P(x \geq 5)\).
03

Compute the probability that \(P(x

To find \(P(x<6)\), we can simply add the probabilities for \(x=0, 1, 2, 3, 4,\) and \(5\) from Table 2.
04

Compute the probability that \(P(x=2)\)

To find \(P(x=2)\), we can directly get the corresponding probability from Table 2 by looking for the probability when the mean is 2.5, and \(x=2\).
05

Compute the probability that \(P(1 \leq x \leq 4)\)

To find \(P(1 \leq x \leq 4)\), we can add the probabilities for \(x=1, 2, 3,\) and \(4\) from Table 2.

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