We worked on the attached problems today in class I am now trying to work through them again for understanding and I am not getting very far. My skills in discretemathematics are not such that I can work through these on my own effectively.

3. Seven points are located in a plane. List the possible numbers of lines determined by these points. Your final answer is simply a list of whole numbers. You should indicate how each comes about.

4. Ten pieces of candy are distributed randomly to three children, Arlo, Burl, and Clovis.
a. What is the probability that Arlo gets no candy?
b. What is the probability that Arlo gets more candy than Burl and Clovis together?

5. In the grid below, we will be interested in the number of paths from point A to point B. A step in a path is either one move to the right or one move up (never moving away from B).

There are three discrete problems here, regarding number of lines determined by points in a plain, probability of candy distribution, and the number of paths between points.

Q1) Use the standard logical equivalences to simplify the expression
(ㄱp ^ q) v ㄱ(pVq)
Q2) consider the following theorem
"The square of every odd natural number is again an odd number"
What is the hypothesis of the theorem? what is the conclusion? give a direct proof of the theorem.
Q3) consider the follo

Construct addition and multiplication tables for arithmetic modulo 11. For example, 7 + 8 mod 11 is
4 and 7*8 mod 11 is 1 so the entry in row 7, column 8 would be 4 for the addition table and 1 for the multiplication table.
Use your tables to solve each of the following congruences:
a. 3x+2≡8 (mod11)
b. 3x-5≡2 (m

Let four random variables X1, X2, X3, X4 have common mean m1=m2=m3=m4= 5 and common variance (sigma 1)^2= (sigma 2)^2= (sigma 3)^2= (sigma4)^2= 6 and common correlation coefficient p(sub ij)= .1, i does not equal j. Determine the mean and the variance of Y=X1 +X2 + X3 + X4

1. Compute the unit-pulse response h[n] for n=0, 1, 2 for the discrete time system
y[n+2] + 1/2y[n+1] + 1/4y[n] = x[n+1] - x[n]
2. Determine if each of the following signals is periodic. If a signal is periodic, what is its period?
x[n] = 3sin(100n)
x[n] = 4cos(1.5πn)
3. For the discrete signals defined as the

What is a probability distribution and its purpose?
Distinguish between discrete and continuous probability distributions. Give an example of each.
What is randomness? Assume you have an Excel worksheet of the dimension, A1:E101. The first row contains data labels. How would you randomize the data file and to select a