(→Problem 3: "Bias" Estimate) |
m (→Problem 4: Votes are In) |
||
| Line 15: | Line 15: | ||
== Problem 4: Votes are In == | == Problem 4: Votes are In == | ||
| + | The election is over and the votes have been cast. The Tippecanoe election officer is lazy however, and decides he is just going to see a 1000 random votes. He does so, and finds 600 for Obama and 400 for McCain. He declares Obama has won Tippecanoe. What is (an upper bound on) the probability that he is wrong? (Assume, as in class, that Tippecanoe has infinite people.) | ||
Revision as of 11:23, 29 October 2008
Contents
Instructions
Homework 8 can be downloaded here on the ECE 302 course website.
Problem 1: Gone Fishin'
On average, it takes 1 hour to catch a fish.
- (a) What is (an upper bound on) the probability that it will take 3 hours?
- (b) Landis only has 2 hours to spend fishing. What is (an upper bound on) the probability he will go home fish-less?
Problem 2: Bounded Variance
All you know about a discrete random variable $ X $ is that it only takes values between $ a $ and $ b $, inclusive (i.e. $ X\in[a,b] $). How large can its variance possibly be? What is the answer if $ X $ is a continuous random variable?
Problem 3: "Bias" Estimate
- (a) You have a coin of unknown bias. You flip it 10 times, and get TTHHTHTTHT as the sequence of outcomes. What is the maximum likelihood estimate of the bias (i.e. the probability, $ p $, of heads)?
- (b) A friend has a coin of unknown bias. He flips it $ n $ times, and finds that $ k $ of them were heads. However, he neglects to record the exact sequence. What is the max-likelihood estimate for the bias in this case?
Problem 4: Votes are In
The election is over and the votes have been cast. The Tippecanoe election officer is lazy however, and decides he is just going to see a 1000 random votes. He does so, and finds 600 for Obama and 400 for McCain. He declares Obama has won Tippecanoe. What is (an upper bound on) the probability that he is wrong? (Assume, as in class, that Tippecanoe has infinite people.)
