# Random Process MCQ’s

This set of Electronic Devices & Circuits Multiple Choice Questions & Answers (MCQs) focuses on “Random Process”.

1. White noise with power density No/2 = 6 microW/Hz is applied to an ideal filter of gain 1 and bandwidth W rad/s. If the output’s average noise power is 15 watts, the bandwidth W is

a) 2.5 x 10 ^{(-6)}

b) 2.5p x 10 ^{(-6)}

c) 5 x 10 ^{(-6)}

d) p5 x 10 ^{(-6)}

2. For random process X = 6 and Rxx (t, t+t) = 36 + 25 exp(|t|). Consider following statements:

(i) X(t) is first order stationary.

(ii) X(t) has total average power of 36 W.

(iii) X(t) is a wide sense stationary.

(iv) X(t) has a periodic component.

Which of the following is true?

a) 1, 2, and 4

b) 2, 3, and 4

c) 2 and 3

d) only 3

3. Air craft of Jet Airways at Ahmedabad airport arrive according to a Poisson process at a rate of 12 per hour. All aircraft are handled by one air traffic controller. If the controller takes a 2 – minute coffee break, what is the probability that he will miss one or more arriving aircraft?

a) 0.33

b) 0.44

c) 0.55

d) 0.66

(Q.3-Q.4) The two-level semi-random binary process is defined by X(t) A or -A where (n 1)T < t < nt and the levels A and -A occur with equal probability. T is a positive constant and n = 0, ±1, ±2.advertisement

4. The auto correlation Rxx(t1 = 0.5T, t2 = 0.7T) will be

a) 1

b) 0

c) A x A

d) 0.5 (A x A)

5. The mean value E[X(t)] is

a) 1/2

b) 1/4

c) 1

d) 0

6. A random process is defined by X(t) + A where A is continuous random variable uniformly distributed on

(0,1). The auto correlation function and mean of the process is

a) 1/2 & 1/3

b) 1/3 & 1/2

c) 1 & 1/2

d) 1/2 & 1

7. A stationary random process X(t) is applied to the input of a system for which h(t) = u(t) t^{2} e^{(-8t)}. If E[X(t)] = 2, the mean value of the system’s response Y(t) is

a) 1/128

b) 1/64

c) 3/128

d) 1/32

(Q.8-Q.9) The auto correlation function of a stationary ergodic random process is shown below.

8. The E[X^{2(t)}] is

a) 10

b) sqrt(10)

c) 50

d) sqrt(50)

9. The mean value E[X(t)] is

a) 50

b) sqrt(50)

c) 20

d) sqrt(20)

10. The variance is

a) 20

b) 50

c) 70

d) 30