Below are very difficult questions. I want all of them solved correctly!

1.Determine the following set of a counter and explain. A single 1, the rest 0

2.What is the equivalence of statement p and q if P<->Q. Give a logical answer.

3.During a sample S denoted by P(a) = 0 it was determined that A does not depend on any other event. True or false?

4.Determine values of P that make F and G independent given that P(f) = 1/5 and P(F or G) = .

5.Determine P(M) + P(N)where P of both occurring together is 0.2 and at least one event occurring is 0.6

6.Solve for the following mutually exclusive events. A = A₁ A₂........ A_n, and A₁...A_n

7.During a phone launch, the probability of good battery life span of phone A was 70% while that of B was 80%. Determine the probability of a phone's battery having a good life span.

8.Suppose women are equal to men, what is the probability of those born colour blind if men are 100 and 1/20 are colour blind while men are 250 and 1/25 are colour blind?

9.Determine the phase associated with DTFS.

10. Determine the spectrum obtained after plotting |ck| as a function of frequency.