Homework 5

Due Mon. Oct. 4 at 11:59pm

Homework policies and submission instructions


  1. (10 points) Textbook problem 4.12
  2. (10 points) Textbook problem 5.9
  3. (10 points)
    1. Textbook problem 5.17
    2. Textbook problem 5.19
  4. (10 points) Suppose you flip a fair coin \( N \) times. Let random variable \( h \) be the number of heads that occur. Use the normal approximation to estimate the following probabilities. Write your answers using integrals. Do not evaluate the integrals.
    1. \( P(h \in [495000,505000])\) given that \(N=10^6\)
    2. \( P(h > 9000)\) given that \(N=10^4\)
    3. \( P(h < 40 \text{ or } h > 60)\) given that \(N=10^2\)
  5. (10 points) Let's say you check the CS 361 ED at the top of the hour every hour (both day and night). The posts arrive independently at an average rate of 0.1 posts per hour, which means that the number of new posts each time you look is a Poisson random variable with intensity \( \lambda=0.1 \). Answer each of the following questions with an expression of form \( Ae^B\) and then do evaluate the expression as a number.
    1. What is the probability that there are no new posts when you look?
    2. What is the probability that there is exactly one new post when you look?
    3. What is the probability that there are exactly two new posts when you look?
    4. Fed up with this unsatisfying routine, you decide to sign up for daily digest emails. What is the probability that on a given day you do not receive a daily digest email at 1pm? In other words, what is the probability that at 1pm there were no new posts in the preceding 24 hours?
  6. (Extra 2 points) Textbook problem 5.8