. An analog communication system with random variable X has probability density function f x( ) defined by

kx⁴,x 1

f x( ) =k(2 x²), 1 x1

kx⁴,x 1

Determine

i. the value of k.[3marks] ii. F x( )[5marks] iii. _x[5marks]

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 figure 3.

Figure 3

i. Draw a transition diagram.[5marks] ii. Write down a transition matrix, P.[4marks] iii. Name the type of matrix in Q3(b)[2marks] iv. P X( ^{2 =2 X1 =1X0 =3)}[3marks]

v. P X( ^{2 =2 X3 =3X0 =2)}[3marks]