---
title: "hw9"
author: "Mark Pearl"
date: "3/12/2020"
output:
  html_document: default
  pdf_document: default
---

```{r setup, include=FALSE}
library('FrF2')
```

## R Markdown

# Question 12.1
Describe a situation or problem from your job, everyday life, current events, etc., for which a design of experiments approach would be appropriate.

If I were to trace this back to sports. A good example of an experiment would be when a company is testing the effectiveness of a new hockey stick when producing a shot. Factors such as player weight, age, strength, technique, etc. We would be able to control these factors to determine their overall effectiveness of the stick. 

# Question 12.2
To determine the value of 10 different yes/no features to the market value of a house (large yard, solar
roof, etc.), a real estate agent plans to survey 50 potential buyers, showing a fictitious house with
different combinations of features. To reduce the survey size, the agent wants to show just 16 fictitious
houses. Use R’s FrF2 function (in the FrF2 package) to find a fractional factorial design for this
experiment: what set of features should each of the 16 fictitious houses have? Note: the output of
FrF2 is “1” (include) or “-1” (don’t include) for each feature.

```{r house}
library('FrF2')
FrF2(nruns = 16, nfactors = 10)
```

From the results we can see that the first combination we should only keep the following features: {A, B, D, E, H}. This same logic can be used to determine which factors to keep from rows (i.e. houses) 2-16. Since we have 10 features and 2 possible expected values, then we can have 1024 permutations or combinations of 16 factor sets.

# Question 13.1
For each of the following distributions, give an example of data that you would expect to follow this distribution (besides the examples already discussed in class).


Answer
i) Bionmial: An example of data that follows the Binomial distribution is a survey of responses to a yes-no question where the probably of responses is known or can be estimated. An example could be a team winning or losing a game.

ii) Geometric: Number of times I take a shot with my hockey stick before my stick breaks. 

iii) Poisson: This distribution is excellent at modeling event occurances over an interval of time. Number of parking tickets issued in the City of Ottawa in the morning between 7 to 9 AM. 

iv) Exponential: This distribution can model the lengths of inter-arrival times between events modeled by the Poisson distribution. An example of this could be the time between parking tickets issued. 

v) Weibull: This distribution is used to model factors where the probability changes over time. An example of this would be the odds of winning a 50 to 50 ticket at a hockey game as the time get closer to the annoucement of the winner. 
