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e. Compute the mean μx. f. Compute the standard deviation ox.

e. Compute the mean μx. f. Compute the standard deviation ox.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Lesson 42: Probability Distribution Analysis** **Fifteen items or less:** This lesson explores the number of customers in line at a supermarket express checkout counter, modeled as a random variable with the following probability distribution. **Table: Probability Distribution** ``` x | 0 | 1 | 2 | 3 | 4 | 5 | P(x)| 0.10 | 0.25 | 0.30 | 0.20 | 0.10 | 0.05 | ``` **Explanation of the Table:** - The random variable \( x \) represents the number of customers in line. - \( P(x) \) provides the probability for each number of customers in line, ranging from 0 to 5. **Questions:** a. **Find \( P(2) \).** - Solution: \( P(2) = 0.30 \) b. **Find \( P(\text{No more than 1}) \).** - Solution: \( P(x \leq 1) = P(0) + P(1) \) - Calculation: \( P(0) + P(1) = 0.10 + 0.25 = 0.35 \) c. **Find the probability that no one is in line.** - Solution: \( P(0) = 0.10 \) d. **Find the probability that at least three people are in line.** - Solution: \( P(x \geq 3) = P(3) + P(4) + P(5) \) - Calculation: \( 0.20 + 0.10 + 0.05 = 0.35 \) e. **Compute the mean \( \mu_X \).** - Solution: \( \mu_X = \sum [x \cdot P(x)] \) - Calculation: \( 0(0.10) + 1(0.25) + 2(0.30) + 3(0.20) + 4(0.10) + 5(0.05) \) - Detailed Calculation: \( 0 + 0.25 + 0.60 + 0.60 + 0.40 + 0.25 =
Transcribed Image Text:**Lesson 42: Probability Distribution Analysis** **Fifteen items or less:** This lesson explores the number of customers in line at a supermarket express checkout counter, modeled as a random variable with the following probability distribution. **Table: Probability Distribution** ``` x | 0 | 1 | 2 | 3 | 4 | 5 | P(x)| 0.10 | 0.25 | 0.30 | 0.20 | 0.10 | 0.05 | ``` **Explanation of the Table:** - The random variable \( x \) represents the number of customers in line. - \( P(x) \) provides the probability for each number of customers in line, ranging from 0 to 5. **Questions:** a. **Find \( P(2) \).** - Solution: \( P(2) = 0.30 \) b. **Find \( P(\text{No more than 1}) \).** - Solution: \( P(x \leq 1) = P(0) + P(1) \) - Calculation: \( P(0) + P(1) = 0.10 + 0.25 = 0.35 \) c. **Find the probability that no one is in line.** - Solution: \( P(0) = 0.10 \) d. **Find the probability that at least three people are in line.** - Solution: \( P(x \geq 3) = P(3) + P(4) + P(5) \) - Calculation: \( 0.20 + 0.10 + 0.05 = 0.35 \) e. **Compute the mean \( \mu_X \).** - Solution: \( \mu_X = \sum [x \cdot P(x)] \) - Calculation: \( 0(0.10) + 1(0.25) + 2(0.30) + 3(0.20) + 4(0.10) + 5(0.05) \) - Detailed Calculation: \( 0 + 0.25 + 0.60 + 0.60 + 0.40 + 0.25 =
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