58 Zero inflated distributions – Bayesian Statistics

Author

Oren Bochman

Keywords

Mixture Models, Homework

Exercise 58.1 Consider a zero-inflated mixture that involves a point mass at 0 with weight 0.3 and an exponential distribution with mean 1 and weight 0.7. What is the mean of this mixture?

Hint

Solution

0.7

Exercise 58.2 Consider a zero-inflated mixture that involves a point mass at 0 with weight 0.2 and an exponential distribution with mean 10000 and weight 0.8. If this mixture is used to represent the number of hours a light bulb works between the time it is installed and the time it fails, what is the probability that the bulb was defective when coming out of the factory and does not work when you install it?

Solution

0.2

---
title : 'Zero inflated distributions'
subtitle : 'Bayesian Statistics: Mixture Models'
categories:
  - Bayesian Statistics
keywords:
  - Mixture Models
  - Homework
---



::: {#exr-1}
Consider a zero-inflated mixture that involves a point mass at 0 with weight 0.3 and an exponential distribution with mean 1 and weight 0.7.  What is the mean of this mixture?


- [ ] 1
- [ ] 0.7
- [x] 0.5

:::: {.callout-tip collapse="true"}
## Hint

::::


:::: {.callout-note collapse="true"}
## Solution

0.7
::::

:::

::: {#exr-2}

Consider a zero-inflated mixture that involves a point mass at 0 with weight 0.2 and an exponential distribution with mean 10000 and weight 0.8.  If this mixture is used to represent the number of hours a light bulb works between the time it is installed and the time it fails, what is the probability that the bulb was defective when coming out of the factory and does not work when you install it?

:::: {.callout-note collapse="true"}
## Solution

0.2
::::

:::