Due January 15
Joint probability table for use in problems 1-6.
p(x=1,y=1) = 0.6 p(x=1,y=2) = 0.1 p(x=1,y=3) = 0.0
p(x=2,y=1) = 0.1 p(x=2,y=2) = 0.1 p(x=2,y=3) = 0.1
1. Compute p(x=1) and p(x=2). Compute E[x].
2. Compute p(y=1), p(y=2), and p(y=3). Compute E[y].
3. Compute p(x|y) for all values of x and y (6 probabilities in all).
4. Compute p(y|x) for all values of x and y (6 probabilities in all).
5. Compute E[x+y] and compare with E[x] + E[y].
6. Compute E[xy] and compare with E[x]E[y].
7. Plot log(1/x) in the range x=[0,1] for base 2, e, 10 on the same
plot.
8. Muliply the following matrix by itself to get M^2. Also compute M^k, for
k = 3, 4, 8. use of a computer program is encouraged for k>2.
0.2 0.1 0.7
M = 0.4 0.4 0.2
0.1 0.1 0.8