This set of Radar Multiple Choice Questions & Answers (MCQs) focuses on “Probability Density Functions”.

1. The measure of the likelihood of the occurrence of an event is called _______

a) statistics

b) randomization

c) probability

d) approximation

View Answer

Explanation: Probability is a measure of the likelihood of the occurrence of an event and it ranges from 0 to 1. Means, an event that is likely to come has a probability of 1 and an impossible event has a 0 probability.

2. By definition, probability density function is always negative.

a) True

b) False

View Answer

Explanation: The probability density function is always positive, by definition. It’s because every measurement generates some value and over all values of x, the integral of the probability density function must be unity i.e. \(\int_{-\infty}^{\infty} p(x)dx=1\).

3. Which of the following is also known as second central moment in the equation?

σ^{2} = (x–m_{1})^{2}_{av}

a) Standard deviation

b) Variance

c) Random variable

d) Mean square value

View Answer

Explanation: Variance σ

^{2}is the mean square deviation of x about its mean m

_{1}expressed in the above equation. It is also called as second central moment.

4. What does k describes in the uniform probability density function, p(x) = k for a < x < a+b?

a) Power of the ac component

b) Statistical phenomena

c) Phase of a random sine wave

d) Average value of pdf

View Answer

Explanation: k describes the phase of a random sine wave relative to a particular origin of time, where the phase of the probability might lie anywhere between 0 to 2π radians.

5. Why is Gaussian probability density function important in detection theory?

a) It enhances the root mean square value

b) It describes many sources of noise

c) The error in numerical computation is rounded off

d) Maximizes the video output

View Answer

Explanation: The Gaussian pdf is important in detection theory because it describes many sources of noise, including receiver thermal noise and also it is more convenient to manipulate mathematically.

6. What is the shape of Gaussian probability density function?

a) Bell shaped

b) Square

c) Straight line

d) Ellipse

View Answer

Explanation: Gaussian probability density function has a bell shaped appearance. It is often referred as normal distribution and is shaped like a bell because the central arc is concentrated with the greatest number of values (the highest number of occurrence of elements) and decreases on either sides.

7. The ability of the Gaussian probability density function to represent many statistical phenomena is a consequence of the _______

a) mean square deviation

b) quantization theorem

c) standard deviation

d) central limit theorem

View Answer

Explanation: Central limit theorem is the ability of the Gaussian pdf to represent many statistical phenomena. It means, the pdf of the sum of large number of independent quantities always approaches to Gaussian pdf no matter what.

8. How is the envelope of a narrowband filter describes as when the input noise voltage is Gaussian?

a) Uniform pdf

b) Rayleigh pdf

c) Exponential pdf

d) Gaussian pdf

View Answer

Explanation: The envelope of a narrowband filter in radar is described by the Rayleigh pdf when the input noise voltage is Gaussian because it is the only continuous probability distribution for random variables with positive values. The distribution was named after Lord Rayleigh.

9. Statistical phenomena can also be represented by the probability distribution function.

a) True

b) False

View Answer

Explanation: Statistical phenomena can also be represented by the probability distribution function P(x), which is related to the probability density function p(x) by P(x) = \(\int_{-\infty}^{x}p(x)dx\).

10. Exponential pdf can also be called as _________

a) Poisson pdf

b) Rayleigh power pdf

c) Rayleigh voltage pdf

d) Log normal pdf

View Answer

Explanation: The exponential pdf is also known by the name Rayleigh power pdf i.e. if the parameter x in the Rayleigh pdf is voltage, then w represents the power and w

_{0}is the average power.

**Sanfoundry Global Education & Learning Series – Radar.**

To practice all areas of Radar, __ here is complete set of Multiple Choice Questions and Answers__.