Assignment #1

Description

In this assignment you’ll have to answer questions based on the presentation Introduction to Probability and Statistics and the lecture Probability distributions and random variables. Also, you may need to check the examples provided by Westfall & Henning (2013) (Chapter 1).

Please submit your answers in a Word document or Libre Office document with a cover page. Copy the question and then answer the question in the following paragraph, similar to this example

1) What is a parameter?

Answer: A parameter is an unknown value in a model, but it will be estimated using the data

In addition, please watch the next video where I explain how to add your R code to your answers CLICK HERE.

Relevant questions related to NATURE

Please answer the following questions, if you find yourself not understanding the question please send me an email or schedule an appointment. My aim is to evaluate if I did a good job communicating the main points, in addition; I aim to evaluate if you understood the content.

1. Let’s imagine that you need a model relating crime rate in a “typical” city to the poverty, then you came up with the next model:

\[\begin{equation} CrimeRate = 60+5*Poverty \end{equation}\]

1.1) What kind of model is this? Provide the right term from the presentation or from page 8 in Westfall & Henning (2013). (10 points)

1.2) Is this model good to study crime? Answer this question based on the lecture or based on page 9 in Westfall & Henning (2013). (10 points)

2. In page 13, Westfall & Henning (2013) define a Purely Probabilistic Statistical Model as:

Important

A purely probabilistic statistical model states that a variable \(Y\) is produced by a pdf having unknown parameters. In symbolic shorthand, the model is given as \(Y \sim p(y|\theta)\)

Based on this definition, please write the name of three probability models we studied in class. (Hint: Check the lecture Probability distributions and random variables CLICK HERE ) (10 points)

3. We studied in class that models generate data, what is the distribution of the following model?, and what information is assumed in the “population model” or data generating process? (10 points)

## Average or mean
Mean <- 50
## Standard deviation
SD <- 20
N <- 2000

generatedValues <- rnorm(n = N, mean = Mean, sd = SD )

plot(density(generatedValues),
     xlab = "generated values",
     ylab = "p(y) or likelihood",
     main = "What is this distribution?")

4. I explained in class that simulations are good for learning complicated topics in statistics. I also mentioned that simulations help to explain the concept of DATA (uppercase) versus data (lowercase). Explain the concept of DATA and data using the example of tossing a coin (10 points). When we simulate one data set using the Bernoulli distribution, is this data set* DATA* or data? (10 points)

5. R contains data sets available for practicing. You can see the list of data sets by running data(). Run the data() function, after that select one data set, then run the function summary(). What information issummary() giving you? (10 points)

### Example: I'm running summary() with the data set named 'mtcars'. Select
### another data set from data()
data()
summary(mtcars)

6. Read the chapter The most important question: how do I import data? from the lab book. You may read it by clicking HERE.

After reading the chapter, please set the working directory in your local computer. Then import the following data set into R: CLICK HERE . Finally estimate the mean life expectancy of year 2019. Your code should look similar to this example:

setwd("write/yourpath/toyour/targetfolder")

lifexp <- read.csv("lifeExpect.csv")

mean(lifexp$X2019)

Include your code, and the output after running the code (15 points).

7. In this exercise, I will introduce a new function in R. The name of this function is pipe. A pipe is a R function that helps to do several steps in one single line of code. It is like creating a chain of multiple steps.

In R, pipes are created using this sign: |>. Let’s see the following example:

library(dplyr)
library(palmerpenguins)

  penguins |>
    filter(species == "Adelie") |>
    select(bill_depth_mm) |>
    with(mean(bill_depth_mm, na.rm = TRUE))

[1] 18.34636

In the code above, I’m performing several steps on the data set named penguins, from the package palmerpenguis. You will see the function filter() from the package dplyr. The function filter() is selecting the penguins classified as “Adelie”, then I’m selecting the column “bill_depth_mm”, and finally I’m estimating the mean of “bill_depth_mm”. As you can see, you can read the pipe as “then do this”. In English you could read: filter penguins by species = “Adelie”, then select the column “bill_depth_mm”, then estimate the mean of “bill_depth_mm”.

Following this explanation, select in the life expectancy data the column “X2019”, after that estimate the mean the the column “X2019”. Include your code, and the output. (15 points)

Previuos step

To answer this question you have to install the package dplyr, by running this code: install.packages("dplyr"). To use the package you have to run first: library(dplyr). You may read this information first: https://blackhill86.github.io/StatsBook/functionsPack.html

Extra points (5 points)

Create a good meme to express how you feel in this class, include your meme in your Word document.

References

Westfall, P. H., & Henning, K. S. (2013). Understanding advanced statistical methods. CRC Press Boca Raton, FL, USA: