Due January 16
Joint probability table for use in problems 1-6.
p(x=1,y=1) = 0.3 p(x=1,y=2) = 0.3 p(x=1,y=3) = 0.1
p(x=2,y=1) = 0.3 p(x=2,y=2) = 0.0 p(x=2,y=3) = 0.0
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].
Problems 7 and 8 refer to the case of
a block code with 6 bits/block (5 message bits, and one parity bit)
used on a transmission line with a probability of failure of p=0.0002
for each bit:
7. What is the probability of zero errors?
8. What is the probability of an undetected error?
9. Compute the logarithm of 10 in bases 10, e, 2, and 3
10. Find the check number (that is, find the value of ?) for the ISBN
(uses a weighted code with base 11):
0-201-10179-?
11. Plot log(1/x) in the range x=[0,1] for base 2, e, 10 on the same
plot.