Solution 3 Computational Intelligence Lab 2015

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Problem 1 (Conditional Probability)

  1. 3/4
  2. 1/4
  3. 1/2
  4. 1/3 (we know one is a girl, so we're left with: girl girl, girl boy, boy girl. One out of these three is girl girl)
  5. 1/3

Problem 2 (Bayes' Rule)

There is an uncommon disease that has infected 1% of the human population. Assume that we have a test for this disease that is positive on an infected person with probability 99% and negative on a healthy person also with probability 99%.

If my test comes out positive, what is the probability that I am infected?


Problem 3 (K-means Theory)


Show that the K-means algorithm solves a matrix factorisation problem by showing that where the matrices are defined as follows: