Tackle the following difficult questions.

1. Give a condition most suitable for the use of Binomial distribution.

2. Denoting probability of success as p and no. of trials as n, determine the mean value in a binomial distribution. Failure is denoted by q.

3. What will be the maximizing value of |z|2/f(z) where f(z) equals |z|2+Re z(2(z+z)+3(z-z)/2i?

4. Given that f(z)=arg 1/(1 - z), determine range f(z) for |z|=1, z1.

5. Explain the value of x given the equation X=x+2 where x=1 and holding the assumption that x=5 is the initial value.

6. Determine and describe the total number of strings given a string of length 4 that contains [0,1] where the two ones are not together.

7. Given the signal to noise ratio which is usually 3162, calculate for the highest bit rate of a regular phone call. Explain

8. Determine the device that is used for the sole purpose of boosting the signal between two cable segments or wireless access points.

9. Determine the bitrate 'r' given that the capacity equals 512 for a message digest of size 256 in SHA-3.

10. Determine and explain the two phases that are involved in the sponge construction.