Unit 10 of 13
Exponential and Normal Models
- 4 lessons
- Videos 64 to 67
Waiting times and measurement errors are often modeled with exponential and normal distributions. This unit computes their probabilities and quantiles and compares models by their assumptions.
The exponential distribution has an exponentially decaying survival probability and is memoryless, so the time already waited does not change the distribution of the remaining wait. A normal distribution is set by its mean and standard deviation, and standardization reduces every normal calculation to the standard normal CDF, both from thresholds to probabilities and from probabilities back to quantiles. The unit ends by choosing among uniform, exponential and normal models from their support, mechanism and tails rather than from the look of a curve.
Every lesson will be one video. The videos are coming soon, and each lesson page already has the definitions and an example for every key term.
Exponential Waiting Times
Exponential Distributions
How the exponential distribution models a waiting time, how its rate and scale differ, and how the survival function, memorylessness and the natural logarithm give tail probabilities and quantiles.
Video 64
Normal Distributions
The Normal Distribution
What a normal distribution is, how its mean and standard deviation shape the normal density, how standardization leads to the standard normal, and how to find central and tail probabilities.
Video 65
Normal Probabilities and Quantiles
How to find normal interval and upper-tail probabilities with z-scores, the standard normal CDF and its symmetry, and how the inverse CDF gives normal quantiles and central probability intervals.
Video 66
Choosing a Continuous Model
Choosing a Continuous Probability Model
How to choose a uniform, exponential or normal distribution family from the mechanism, the support and the tail behavior, why the parameter convention matters, and how model adequacy differs from a correct calculation.
Video 67