Suppose that your goal is to automatically detect whether a subject has a brain tumor by processing MRI scans and measuring the size of a specific section of the brain (hydrocephalus). Assume that we have already collected some data on the size of 201 subjects where half of them did not have a tumor. The collected data is as the following: Hydrocephalus size of 10 subjects without tumors w,:

3 5 3.4 6 5.5 3 7 2.9 4.3 4.8

Hydrocephalus size of 10 subjects with tumors w:

4 5.5 6.4 7.8 6.9 7 8.5 4.3 5.6 9

Use Python syntax "mean" and "var" to find the mean and variance of the collected data. Assume that the size of hydrocephalus has a Gaussian distribution and usually 1/3 of people who are ordered an MRI by a neurologist for tumor diagnosis really have a tumor. Plot the posteriori and corresponding decision regions for tumor detection.