stat310

Homework 03

This homework follows the standard late penalty: 0% if in the stat310 mailbox by Thursday 2 Feb 4pm, 10% by 5pm the following day, 100% otherwise. Please read the syllabus for other homework policies.

  1. (2 pts each) For each of the following random variables, identify the distribution (including the parameters) that most closely matches the situation. Justify your choice. What assumptions do you have to make?

    1. On average, Houston Metrorail comes every 10 minutes. Let \( X_{1} \) be the amount of time I have to wait for the next train to come.

    2. A couple is trying to get pregnant. Assume that the chance of getting pregnant from trying once is 2.2%. Let \( X_{2} \) be the number of times they try before they are successful.

    3. The Patriots and Giants are playing in the super bowl. Let \( X_{3} \) be the Patriots’ score minus the Giants’ score.

    4. I flip a coin. Let \( X_4 \) be one if I flip a head, zero otherwise.

    5. I am a lazy grader, so instead of reading your homeworks, I use a spinner labelled with the numbers 3 through 19. Let \( X_{5} \) be your grade calculated using this method. (PS. This is not how I really grade).

    6. Under Auckland there are 50 volcanos. The average rate of eruption is about 11 every 100,000 years. Let \( X_{6} \) be the number of eruptions in the next 100 years.

  2. (2 pts each) Compute the constant \( c \) so that following functions are probability mass functions (pmf).

    • \( f_{1}(x)=c_1 \cdot \log(x), x = 1, 2, …, 5 \)
    • \( f_{2}(x)=c_2 x^{2}, x = 1, 2, …, n \)
    • \( f_{3}(x)=c_3 / x^{3}, x = 1, 2, … \)
    • \( f_{4}(x)=c_4 / x^{2}, x = 1, 2, … \)

  3. (8 pts) Calculate the expected values of random variables \( Y_{1}, Y_{2}, Y_{3}, Y_{4} \) having pmf’s \( f_{1}, f_{2}, f_{3}, f_{4} \) respectively.

  4. (2 pts Bonus credit) Given an arbitrary function f, how can you turn in into a pmf? What restrictions do you need to put on f?

  5. Extra credit: (5pts)

    1. Attend Rob Tibshirani’s lecture, January 30, 2012, 4-5pm in Duncan Hall’s McMurtry Auditorium.

    2. Write 2 paragraphs about what you learned and how it relates to Stat310.