1 In a communication network, point A sends a signal to point B, which relays the signal to point C. I here is a probability of 0.2 that there will be an error in the signal from A to B. There is a 0.7 probability of an error in the signal from B to C. What is the probability of receiving the wrong signal sent from A to C?

2. Suppose that 15 employees are to be divided among 4 jobs, with 6 employees going to job I, 5 to job II, 2 to job III, and 2 to job IV. In how many ways can the lob assignment be made?

3. On a surprise quiz with two questions, the first question is multiple choice with three alternatives a, b, and c. while the second question is true-false type. Suppose a student is completely unprepared for the quiz, and so decides to answer at random.

a. Describe a suitable sample space. 2

b. If the correct answer is (b,T), find the probability that:

1. Both questions are answered correctly 1
2. The first question is answered correctly 1
3. At least one is answered correctly 1
4. At most one is answered Correctly 1

4 A random variable X has the probability density:

Fx(x) = {bx -2

             { elesewhere}

Determine the value of b and the mean value of the function g(X) = 4X²

5. The joint density function of two random variables X and Y is:

 fxx(X,Y) = c u (x)u(y)e^-(2x+y(y))

Determine c and whether the two random variables are statistically independent.

6. A wide-sense stationary random process X(t) has a power of E{X2(t)}=4. Give at least one( that means one or more if they exist )

reason why the following experssions cannot be its autocorrelation function:

a. Rxx(t,t+ζ ) = 4exp[.2 ζ³ - |ζ|]

b. Rxx(t,t+ζ ) = (-1.0+u(ζ ) / (1+8ζ⁴)

7. Find the power density spectrum for a random process that has the autocorrelation function given by Rxx( ζ) = (A₀2/2)sin(w₀ζ ).