Question 3 a. An analog communication system with random variable X has probability density function f (3:) dened by lax4, x 1 Determine i. the value of k. [3marks'] ii. F(x) [5marks] iii. a; [5marlcs] iv. Sketch the graph of f (x) and F (x). [5marks] b. Consider a communication channel where each substation transmits and receive data. The probability between the substations is shown in gure 3. 2 3 Figure 3 i. Draw a transition diagram. [5 marks] ii. Write down a transition matrix, P. [4marks] iii. Name the type of matrix in Q3(b) [2marks] iv. P(X2 = 2 X1 =1|X0 = 3) [3marks] v_ P(X2 = 2 X3 = 3|XD = 2) [3mm]