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?
