Probability Assignment#

To get full credit in this assignment you need to use numpy, scipy and pandas libraries. Sometimes you need to type equations - type equations in Latex math notation. To produce the plots you can use any plotting library you need.

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Problem 1 (80 points)#

A surgeon analyzes surgical videos and models events that occur. He describes the problem statement in here. Your job is to replicate the solution in Python and demonstrate your understanding of the steps performed by including adequate explanation of the code in either markdown cells or inline to the code. You can insert as many markdown or code cells you need to perform the analysis.

Question 1a (10 points)#

Write the code for generating the gs variable. This is the simplest random variable of the problem and can be generated independent of the others.

# Code here

Question 1b (20 points)#

We have three variables, ak, pp, and ptime. Write the code for generating these variables from Multivate Gaussian distribution and replicate the associated plots.

# Code here

Question 1c (20 points)#

Perform the probability inrtegral transform and replicate the associated plots.

# Code here

Question 1d (20 points)#

Perform the inverse transform sampling.

#Code here

Question 1e (10 points)#

Replicate the final plot showcasing the correlations between the variables.

#Code here

Problem 2 (20 points)#

You now pretend that the \(n=4\) dimensional data you generated in Problem 1 arrive sequentially one at a time (the co-called online learning setting). Introduce the index \(i\) to represent the ith arriving data sample \(\mathbf x_i\).

  1. Write the expression of the sample correlation matrix (5 points)

  2. Write the expression of the sample correlation matrix that can be estimated recursively and plot the elements of the sample correlation matrix from \(i=1\) to \(i=100\) (15 points)

#Code here