1. Verify that the distance defined via the cardinality between the symmetric difference of two sets obeys the axioms of distance measures.

2. Calculate the edit distance between words 'makk' and 'kakao' using the table filling dynamic programming approach!

3. Calculate the cosine similarity/distance of the vectors x=[3, 4, 5, 6] and y =[4, 3, 2, 1].
What would be our estimation for the angle between the two vectors if we performed their projections to the random vectors v_1=[1, -1, 1, 1], v_2=[-1, 1, -1, 1] and v_3=[1, 1, -1, -1]?
How would our estimation differ if we applied the projection of the two vectors using all the possible vectors consisting of 1s and -1s? (You can use generateAllBinaryOutcomes.m to do so.)

4. Using generate_mvn.m function generate random samples from a multivariate normal distribution with mu=[10 3] and covariance of [4 -4; -4 5].

5. We know that some data comes from a bivariate normal distribution with a covariance of [1.5 v; z 6]. We further know that the Pearson correlation between the two variables in the data is supposed to be 0.8. What are the values for v and z?
Verify the correctness of our solution using Octave!
Generate 5000 points from the covariance matrix you just found out havin mean of [0 0]!
Visualize these points using the generate_mvn.m function and perform whitening of the data points (i.e. make the data uncorrelated)!