(→Problem 2: Bounded Variance) |
(→Problem 3: "Bias" Estimate) |
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== Problem 3: "Bias" Estimate == | == 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, <math>p</math>, of heads)? | ||
| + | *(b) A friend has a coin of unknown bias. He flips it <math>n</math> times, and finds that <math>k</math> 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 == | == Problem 4: Votes are In == | ||
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?
