This assignment will involve writing several Python functions. You should save all of your functions in a single Python module named lastnameFuncs (where lastname is your last name). The module should have a comment block at the top, containing the file name, your name, the date, and a brief description. Each function should also have a doc string that describes it behavior.

This assignment is to be completed on your own, with assistance from the instructor as needed.

1. HW2 Rewrites

For the first part of this assignment, you will rewrite code from HW2 in function form. In particular, you will repackage your code into the following functions:

• expectedRecord: takes two inputs, the runs scored and runs allowed by a team, and returns the expected win-loss record for that team (as calculated by Bill James' Pythagorean formula). For example, expectedRecord(649, 577) would return the string "90-72".
• relativeTime: takes two inputs, a distance (in light years) and a velocity (in percentage of light speed), and returns the relative time for traveling that distance at that speed. For example, relativeTime(309, 50) would return 267.60184976939155.
• timeTable: takes one input, a distance (in light years), and prints a table of the relative times for traveling that distance at various percentages of light speed (10%, 25%, 50%, 75%, 90%, and 99%). This function should call the relativeTime function.

2. Random Sequences

The following Python function can be used to generate a random 3-letter sequence:

• Modify this function so that it has a parameter specifying the desired length of the random sequence. For example, randomSequence(5) should return a random 5-letter sequence, whereas randomSequence(7) should return a random 7-letter sequence.

Using your randomSequence function, it should be possible to approximate the number of words in the English language of a given length. For example, if you generated 10,000 random 4 letter sequences and determined that 100 of those sequences were words, you could estimate a 1/100 ratio of words to sequences. Since there are 26⁴ = 456,976 different 4-letter sequences, you can estimate the number of 4-letter words as round((1/100) * 456,976) = 4,570.

• Download the dictionary.py module and save it in the same folder as your code module. This module contains a function that determines whether a letter sequence is an actual word in a (rather extensive) online dictionary. For example, after importing this module, dictionary.isWord("banana") would return True whereas dictionary.isWord("bununu") would return False.
• Utilizing this helper function, write a function named howManyWords that takes a single input, the word length, and returns an approximation of how many words there are of that length. Your function should use the above approach: generating 10,000 random sequences, counting the number of words (using dictionary.isWord), and multiplying the word-to-sequence ratio by the number of possible sequences of that length.