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3.2.2 Examples of Uniform Distribution

3.2.2 Examples of Uniform Distribution

Overview

This section provides practical examples demonstrating how the uniform distribution can be applied in real-world scenarios, emphasizing its utility in modeling evenly distributed outcomes over a specific interval.

Key Concepts

  • Uniform Distribution in Real Life: Showcases how to model various real-life situations with uniform random variables.
  • Probability Calculations: Discusses how to compute probabilities for events within the defined uniform distribution interval.
  • Percentile Calculations: Explains how to determine percentiles within the uniform distribution framework.

Detailed Explanation

Example 1: Mobile Phone Battery Life

Context: Meena Desai's new Samsung Galaxy phone battery life varies uniformly between 8 to 12 hours.

Probabilities:

  • Probability of needing recharge in 9 hours or less:

  • F(9) = (9 - 8) / (12 - 8) = 0.25

  • Probability of lasting at least 11 hours:

  • F(11) = (12 - 11) / (12 - 8) = 0.25

80th Percentile Calculation:

The time by which 80% of the battery lives end before needing a recharge is 11.2 hours.

Theoretical Discussion

  • Definition of Percentiles for Random Variables: Percentiles are calculated by setting the CDF equal to the desired percentile value.
  • Inverse Calculation of CDF: Demonstrates the calculation process to find specific time points like the 80th percentile.

Discrete vs. Continuous Uniform Distributions

  • Comparison: Highlights the similarities and differences between discrete and continuous uniform distributions.
  • Example of Discrete Uniform Distribution: Discusses the distribution of outcomes when rolling a fair die—each outcome from 1 to 6 has an equal probability of 1/6.

Practical Implications and Calculations

  • Visualizations:

    • Diagram Recommended: Graphs of PDF and CDF for the battery life example.
    • Tabular Representation: Display calculations for different probabilities and percentiles.

  • Discussion: Emphasize the importance of understanding uniform distribution for modeling scenarios with evenly spaced outcomes and its implications in decision-making processes.

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