Assignments


Homework06: (complete by Monday November 4)

For the math problems, scan your handwritten work to one .pdf file. For the code problems, if you are using Colab, submit a .docx file containing the shared link to your Colab Notebook.


Homework05: (complete by Monday October 14)

For the math problems, scan your handwritten work to one .pdf file. For the code problems, if you are using Colab, submit a .docx file containing the shared link to your Colab Notebook.

Additional Exercise 1: (L.L.N.) Demonstrate the Law of Large Numbers for the Normal Distribution.

Additional Exercise 2: (C.L.T.) Demonstrate the Central Limit Theorem for the Normal and Exponential Distributions.

Additional Exercise 3: Demonstrate the independence of the sample mean and sample variance when sampling from the \(Normal(\mu = 5, \sigma^2 = 2^2 = 4)\).


Homework04: (complete by Monday September 23)

For the math problems, scan your handwritten work to one .pdf file. For the code problems, if you are using Colab, submit a .docx file containing the shared link to your Colab Notebook.


Homework03: (complete by Monday September 16)

For the math problems, scan your handwritten work to one .pdf file. For the code problems, if you are using Colab, submit a .docx file containing the shared link to your Colab Notebook.

Hint: For 2.27, assume that a stick being randomly broken at two spots is equivalent to randomly selecting two points on a stick. Assume the length of the stick is 1. Assume that the two points are uniformly distributed on the stick. What is the probability that the three pieces can form a triangle?

Try using Colab Generate to produce Python code to simulate the probability of the three pieces forming a triangle. You can use the following code Prompts to get started.

Prompts

  1. prompt: Using Python code simulate data from a bivariate distribution where the input variable has a Poisson distribution with mean 100 and the distribution of X given N is Binomial with p = 0.95. Plot a scatterplot of the simulated data.

  2. prompt: Fit a linear regression model to the data.

  3. prompt: Fit the same model without an intercept term.

  4. prompt: Compute the mean and standard deviation of the X data.

  5. prompt: Make prediction of X given N = 75 and N = 120.


Homework02: (complete by Wednesday September 4)

For the math problems, scan your handwritten work to one .pdf file. For the code problems, if you are using Colab, submit a .docx file containing the shared link to your Colab Notebook.

Additional Exercise 1: Using Python verify that these models are the same: GAMMA(\(\alpha = n/2, \beta = 1/2\)) = CHISQ(\(n\)). To show this compute the cumulative probabilities for the two models using the same value of \(x\) and parameter \(n\).


Homework01: (complete by Monday Aug. 26)

For the math problems, scan your handwritten work to one .pdf file. For the code problems, if you are using Colab, submit a .docx file containing the shared link to your Colab Notebook.