Question from 8.3: Variance and Standard Deviation Find the variance of the probability distribution for the histogram shown. 0.3 0.2 0.1 1 Th 2 3 4 5 X
Question from 8.3: Variance and Standard Deviation Find the variance of the probability distribution for the histogram shown. 0.3 0.2 0.1 1 Th 2 3 4 5 X
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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Transcribed Image Text:**Question from 8.3: Variance and Standard Deviation**
**Problem Statement:**
Find the variance of the probability distribution for the histogram shown.
**Histogram Explanation:**
- The x-axis is labeled with values from 1 to 5, representing the possible outcomes of a discrete random variable.
- The y-axis represents probabilities, ranging from 0 to 0.3.
- The histogram consists of five vertical bars:
- The bar at x = 1 has a height of 0.2.
- The bar at x = 2 has a height of 0.2.
- The bar at x = 3 has a height of 0.1.
- The bar at x = 4 has a height of 0.3.
- The bar at x = 5 has a height of 0.2.
**Instructions:**
Use the information from the histogram to calculate the variance of the probability distribution.
Expert Solution
Step 1
Solution:
From the given histogram the probability distribution of X is
| c | 1 | 2 | 3 | 4 | 5 | Total |
| f(x) | 0.2 | 0.2 | 0.1 | 0.3 | 0.2 | 1.0 |
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