## Goals

Review Javascript, particularly functional programming. Functions can return functions, and can take functions as arguments. Practice simulating from random processes. Practice iteration with for-loops and updating web elements from Javascript. Experiment with a strange set of dice created by Bradley Efron, whom we will meet again.

Your work should be in the form of an HTML le called index.html with one [p] element per problem. Wrap any Javascript code for each problem in a script element. For example:

Create a zip archive containing this le and upload it to CMS.
For each problem, you may use your work from the previous problem (though you don’t have to). Do not use any other libraries or resources.

## Die simulator

Write a function called roll that returns a random value from [1, 2, 3, 4, 5, 6], with equal (uniform) probability. Run this function 10 times and display the results in the p tag for this problem. The function join on an array may be useful when displaying results.

## Weird die simulator

Write a function called diceFactory that takes one argument, an array called values, and returns a function. This returned function should work the same way as your roll() function, but return a uniform sample from the values array rather than digits from 1-6. Create a function rgb by calling diceFactory([“red”, “blue”, “green”]). Run the rgb function 10 times and display the results in the p tag for this problem.

## Non-transitive dice generator

I recently got some fun conference swag: non-transitive dice. These are four six-sided dice that have the following face values:

``````[1, 1, 1, 5, 5, 5] [0, 0, 4, 4, 4, 4] [3, 3, 3, 3, 3, 3] [2, 2, 2, 2, 6, 6]
``````

We’ll call these E0, E1, E2, and E3 in honor of their inventor, Bradley Efron. Write a new dice-rolling function generator function called nonTransitiveFactory that returns a function that simulates one of these dice. The generator function should take one argument, a number from {0, 1, 2, 3}, that species which die to return. Use the generator function to create a dice-rolling function oneFive that samples from E0. Run this function 10 times and display the results in the p tag for this problem.

## Rolling many times

Write a function called rollNTimes that takes three arguments, two dice-rolling functions (i.e. functions returned by your nonTransitiveFactory function) and a number n. It should “roll” the two dice n times and return the number of times the rst function returned a value greater than the second function. Run this function 10 times with E0 and E1 with n=100, and display the results in the p tag for this problem.

## All pairs comparison

Now create a 4x4 table where each cell has a distinct id attribute. For each possible pair of dice i, j, set the value in the appropriate table cell to the result of calling rollNTimes with the appropriate functions, and with n=1000. It’s ok to compare a die to itself and to display both symmetrical pairs. In the p tag for this problem describe why these are called non-transitive dice.