# 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.