Problems

1. Derive equation 2.17.

Hint: Take the derivative of the sum of squared errors with respect to the two parameters, set them equal to 0, and solve these two equations in two unknowns as:

2. Assume a disease so rare that it is seen in only one person out of every million. Assume also that we have a test that is effective in that if a person has the disease, there is a 99 percent chance that the test result will be positive; however, the test is not perfect, and there is a one in a thousand chance that the test result will be positive on a healthy person. Assume that a new patient arrives and the test result is positive. What is the probability that the patient has the disease?
3. Show that as we move an item from the consequent to the antecedent, confidence can never increase: confidence(ABCD) confidence (ABCD).
4. Let us say that we toss a fair coin ten times. What is the probability that we see four to six heads? What is the probability that we see forty to sixty heads when we toss it one hundred times?
5. Write the log likelihood for a multinomial sample and show equation

4.6.

6. Show equation 5.11.

Hint: Consider multivariate normal distribution and use covariance matrix as

Homework 1 Programming

Python Tutorial and Naive Bayes Classification

Part I. Python Tutorial

1. Download Anaconda Individual Edition installer and follow the installing instructions.
2. After the installation is complete, launch Spyder. Choose File > Open and open the file py in the downloaded folder from eeclass. Then you will see the script.
3. In this homework, you will have to use libraries including numpy and sklearn. To install python libraries, please launch Anaconda Prompt and enter the following command: pip install <library_name>

For example, pip install numpy

You can also install multiple libraries at the same time: pip install numpy sklearn

4. After installing required libraries, please go back to Spyder. Click Run File in Spyder and you will see some messages shown in the Console.
5. Click Variable explorer and you will see the information of variables. Double click any variable and observe its data arrangement.

Part II. Naive Bayes Classification