# Digital Communications Questions and Answers – Random Signals

This set of Digital Communications Multiple Choice Questions & Answers (MCQs) focuses on “Random signals”.

**1. Random process is a function of ______**

**a) Random event and time**

b) Random event and frequency

c) Random event and real number

d) None of the mentioned

**Explanation:** A random process is defined by two variables: a random event and the time at which it occurs.

**2. A random process is called as stationary in strict sense if**

**a) Its statistics vary with shift in time origin**

b) Its statistics does not vary with shift in time origin

c) Its autocorrelation vary with shift in time

d) Its autocorrelation does not vary with shift in time

**Explanation:** If the statistics of a random process change with a change in time origin, it is said to be stationary in a strict sense.

**3. For a stationary process, autocorrelation function depends on**

a) Time

**b) Time difference**

c) Does not depend on time

d) None of the mentioned

**Explanation:** If the statistics of a random process change with a change in time origin, it is said to be stationary in a strict sense.

**4. The autocorrelation function is maximum at**

**a) Origin**

b) Infinity

c) Origin & Infinity

d) None of the mentioned

**Explanation:** When different values are substituted in the formula for the autocorrelation function, the maximum value is found near the origin.

**5. Standard deviation is ______**

a) Rms value of dc

**b) Rms value or ac**

c) Either ac or dc

d) Neither dc nor ac

**Explanation:** The standard deviation of a random variable gives the rms value of an ac component.

**6. The average power of white noise is**

a) Zero

b) Unity

**c) Infinity**

d) Between zero and one

**Explanation:** The average power of white noise is infinity because its bandwidth is infinite.

**7. White noise has _____ mean and ______ variance.**

a) Zero and zero

b) Finite and zero

**c) Zero and finite**

d) One and zero

**Explanation:** White noise is a function with infinite average power, finite variance, and unlimited bandwidth that has a zero mean.

**8. Random variables give relationship between ____**_

a) Two random events

b) Probability of occurence of two random events

**c) Random event and a real number**

d) Random event and its probability of occurrence

**Explanation:** A random variable gives a functional relationship between a random event and a real number.

**9. The distribution function of random variable is**

**a) P(X less than or equal to x)**

b) P(X greater than or equal to x)

c) P(X less than x)

d) P(X greater than x)

**Explanation**: The chance that the random variable’s value is less than or equal to the real number x is the distribution function of the random variable.

**10. The distribution function of -(infinity) and (infinity) is _____**

**a) 0 and 1**

b) 1 and 0

c) Both 0

d) Both 1

**Explanation:** F(minus infinity) is 0 and F(infinity) is 1.

**11. The value of the probability density function of random variable is**

**a) Positive function**

b) Negative function

c) Zero

d) One

**Explanation:** The probability density function is never equal to zero. It’s a non-negative function having a one-dimensional area.

**12. Which gives the measure of randomness of the random variable?**

a) Mean

**b) Variance**

c) Standard variance

d) Pdf

**Explanation:** The randomness of a random variable is measured by its variance. It’s the difference between the square of the mean and the mean square value.

The lack of predictability characterises a random or stochastic signal. In contrast to a deterministic signal, whose value at every instant is known, the value of a random signal at any instant is unknown and cannot be anticipated based on previous values. There are two types of signals: deterministic and random signals. The phrase “random signal” is most commonly used to refer to signals that have a random source. Thermal noise, which is caused by the random movement of electrons in an electric conductor, is one example.