A key focus of our class this week has been “distributions”. A distribution is simply an arrangement of values of a variable such as the population size of a state. A “probability distribution,” is an arrangement of all the values (potential outcomes) of a variable that reflect the frequency of those values in nature. A distribution can either be empirical, which means that it is an actual bunch of numbers, or it can be theoretical, in which case we are just imagining an ideal arrangement of numbers. The normal or “bell” curve is just such a theoretical distribution.

Step 1: Write, test, and submit the necessary code in R

The R open source statistical system is great at creating empirical distributions that are made up of randomly generated numbers. The book includes several commands and explanations of randomly generated distributions. Lets work on creating a normal distribution using R and then work on creating a function provides more information about the distirbution.

# 1. Generate a normal distribution of 1000 samples, with a mean of 80

# 2. Write a function that takes three arguments – a vector, a min and a max, and returns the percentage of elements in the vector that are between the min and max (including the min and max)

# 3. Use the function to see how many of your normal distribution samples are between the range of 79 to 81 

# 4. Repeat 3 times, to see if the results vary.

Step 2: Write, test, and submit the necessary code in R

We can explore called a “Pareto” distribution. We can use R to generate a Pareto distribution of state populations that may be quite similar to the populations of the actual U.S. states. In other words, we can generate random numbers for the sizes of the Fictional States of America (FSA). You can use ??


# 1 & 2. Generate 51 random numbers in a Pareto distribution and assign them to a variable called “FSApops.” Specify a “location” and a “shape” for your Pareto distribution that makes it as similar as possible to the actual distribution of state populations. 

# 3. Create a histogram that shows the distribution of values in FSApops. Hint: hist()

# 4. Report the actual mean and the actual standard deviation of the 51 values stored in FSApops. 

# 5. Report the population of your largest fictional state (i.e., your California) and your smallest fictional state (i.e., your Wyoming). 

Hints:

Learning Goals for this activity:

A. Generate random numbers in a Pareto distribution and assign a variable name.
B. Specify a “location” and a “shape” for a distribution to conform to a model.
C. Create a histogram depicting a distribution of values.
D. Use R commands to report mean and standard deviation.
E. Use appropriate R command to report the most extreme values of a variable.

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