## Contents

## Instructions

Homework 9 can be downloaded here on the ECE 302 course website.

## Problem 1: Imperfect camera

A photodetector has a probability $ p $ of capturing each photon incident on it. A light source is exposed to the detector, and a million photons are captured. What is the ML estimate of the number of photons actually incident on it?

- Problem 1 - Suan-Aik Yeo_ECE302Fall2008sanghavi
- Problem 1 - Beau Morrison_ECE302Fall2008sanghavi
- Problem 1 - Shao-Fu Shih UPDATED_ECE302Fall2008sanghavi
- Problem 1 - Virgil Hsieh_ECE302Fall2008sanghavi
- Problem 1 - Gregory Pajot_ECE302Fall2008sanghavi
- Problem 1 - Jaewoo Choi_ECE302Fall2008sanghavi
- Problem 1 - Joe Gutierrez_ECE302Fall2008sanghavi
- Problem 1 - Anand Gautam_ECE302Fall2008sanghavi
- Problem 1 - Hamad Al Shehhi_ECE302Fall2008sanghavi
- Problem 1 - Tiffany Sukwanto_ECE302Fall2008sanghavi
- Problem 1 - Zhongtian Wang_ECE302Fall2008sanghavi
- Problem 1 - Chris Rush_ECE302Fall2008sanghavi

## Problem 2: Imperfect Radar

A radar works by transmitting a pulse, and seeing if there is an echo. Ideally, an echo means object is present, and no echo means no object. However, some echoes might get lost, and others may be generated due to other surfaces. To improve accuracy, a radar transmits $ n $ pulses, where $ n $ is a fixed number, and sees how many echoes it gets. It then makes a decision based on this number.

Let $ p_1 $ be the probability of an echo for a single pulse when there is no object, and $ p_2 $ be the probability when there is an object. Assume $ p_1 < p_2 $. What is the max-likelihood estimation rule for whether the object is present or absent?

## Problem 3: Exponential Parameter Estimation

The parameter of an exponential random variable has to be estimated from one sample. What is the ML estimator? Is it unbiased?

- Problem 3 - Nicholas Browdues_ECE302Fall2008sanghavi
- Problem 3 - Arie Lyles_ECE302Fall2008sanghavi
- Problem 3 - Katie Pekkarinen_ECE302Fall2008sanghavi
- Problem 3 - Patrick M. Avery Jr._ECE302Fall2008sanghavi
- Problem 3 - Henry Michl_ECE302Fall2008sanghavi Question
- Problem 3 - Divyanshu Kamboj_ECE302Fall2008sanghavi
- Problem 3 - Ken Pesyna_ECE302Fall2008sanghavi

## Problem 4: Uniform Parameter Estimation

$ X $ is known to be a uniform random variable, with range $ [-a,a] $. However, the parameter $ a \geq 0 $ is unknown, and has to be estimated from $ n $ samples. What is the ML estimator? Is it unbiased?

- Problem 4 - Brian Thomas_ECE302Fall2008sanghavi
- Problem 4 -Joon Young Kim_ECE302Fall2008sanghavi
- Problem 4 - Seraj Dosenbach_ECE302Fall2008sanghavi
- Problem 4 - Shao-Fu Shih_ECE302Fall2008sanghavi
- Problem 4 - Junzhe Geng_ECE302Fall2008sanghavi