11 Bayesian learning

Introduction to Bayesian probabilities.

• Estimation of the value of old coins based on the weights of the sub-set of a bag of coins.
• 0.5 points
• submit your solution to BRUTE lab11quiz by May 06, midnight
• format: text file, photo of your solution on paper, pdf - what is convenient for you
• solution will be discussed on the next lab
• Students with their family name starting from A to K (included) have to solve and upload subject A , while students with family name from L to Z have to solve and upload subject B

Although I don't have any symptoms yet, I'm worried about disease X. I'm considering getting tested for it, but haven't yet. I therefore want to study the following phenomena:

• $X$ - the person is sick (has disease X)
• $\bar X$ - the person is healthy (does not have disease X)
• $\ominus$ - the test for disease X came out negative (according to the test, the person does not have disease X)
• $\oplus$ - the test for disease X came out positive (according to the test, the person has disease X)

For the test I'm considering taking, the manufacturer says it has 90% accuracy for both healthy and sick people. The prevalence of disease X in the population is 5%. Try to answer the following questions:

1. What is the probability that a person randomly selected from the population has disease X?
2. What is the probability that I have disease X?
3. How to understand (and denote) test information from the manufacturer?
4. What is the probability that I have disease X if I test positive?
5. What is the probability that I have disease X if I test negative?

Introduction to Bayesian probabilities on estimation of gender of people if we know the weight distribution of male and female colleagues (see pdf).

Start working on the machine learning assignment