Homework Set 7

Submitting Your Work

Your work must be submitted to Anchor for degree credit and to Gradescope for grading.

For any work completed outside of GitHub or Gradescope:

  1. Typeset your work in LaTeX.
  • You should use \begin{enumerate} to create a numbered list, and your solutions to each problem should match with the corresponding number on the assignment.
  • For example, if an assignment has 10 numbered problems, your enumerate should have 10 \item commands, with your solution(s) to problem 1 under the first \item, problem 2 under the second and so on.
  • If you skip a problem, just leave the \item blank, otherwise the numbers of your solutions will not match the assignment document. Here is an example Overleaf document showcasing this format.
  1. Compile into a PDF. This can be done easily through an Overleaf account, otherwise you will need to install LaTeX.
  2. Submit the pdf to Gradescope via the appropriate submission link for the course.
  3. Upload the pdf to Anchor using the form below.

Note: Anchor submissions can occur at any time during the term, but it is critical that you upload all of your work to Anchor before the last day of the term. Gradescope submissions must be submitted before the deadline (or the late deadline, if applicable).

ChatGPT/AI

Use of ChatGPT/AI is forbidden for all assignments in this course.

It is required that all assignments are submitted as a PDF generated from a LaTeX document.

Assignments submitted in any other form will earn zero credit.

Problems

  1. Assume $X$ is a random variable representing the outcome of rolling a standard, fair 10-sided die. a. What are all the possible values $X$ could hold?

    b. What is the expected value of $X$ ($E[X]$)?

    c. What is the variance of $X$?

    d. What is $P(X < 6)$?

    e. What is $P(X < 11)$?

    f. What is $P(X = E[X])$?

  2. Find the mean, median, mode, and range of the following set of numbers. Does the distribution look familiar?

7, 5, 6, 7, 6, 2, 4, 3, 5, 2, 7, 5, 9, 9, 7, 12, 5, 5, 9, 8, 9, 4, 7, 10, 7, 3, 8, 9, 5, 4, 7, 7, 2, 11, 8, 5, 9, 8, 8, 11, 3, 6, 4, 7, 8, 8, 12, 6, 5, 7

  1. Write a function to calculate the mean of a list of numbers, and a function that would calculate the median of a set of numbers. Feel free to use this function to determine the answers to problem 1.

  2. Find the prime factorization of the following numbers a. 456

    b. 2024

    c. 2970

    d. 8910

    e. 2197.

  3. Compute the following: a. $501_8$ + $427_8$

    b. $324_7$ + $324_7$

    c. $412_7$ - $362_7$

    d. $324_7 \cdot 2_7$

    e. $324_7 \cdot 10_7$.

  4. Find a divisibility rule for numbers divisible by 6 in

    a. Base 5

    b. Base 6

    c. Base 7