In this article, we are going to learn about the Random Variables MCQs for ESE.

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**Random Variables MCQs For ESE**

**Q.1 A system has a receiver noise resistance of 50\Omega. it is connected to an antenna with an input resistance of 50\Omega. The noise figure of the system is**

- (a) 1
- (b) 2
- (c) 50
- (d) 101

**Q.2 Which one of the following types of noise gains importance at high frequency?**

- (a) Shot noise
- (b) Random noise
- (c) Impulse noise
- (d) Transit-time noise

**Q.3 Fading is**

- (a) change in polarization only at the receiver end
- (b) change in frequency only at the receiver end
- (c) fluctuation in signal strength at the receiver
- (d) change in phase only at the receiver end

**Q.4 Thermal noise is passed through an ideal low-pass filter having a cutoff at f _{c }= w Hz. The autocorrelation value of the noise at the output of the filter is given as**

- (a) A delta function at t = 0
- (b) Gaussian over the range -\infty \leq t \leq \infty
- (c) Sinc function over the range -\infty < t < \infty
- (d) Triangular function over the range -\frac{1}{2w}\leq t \leq \frac{1}{2w}

**Q.5 A random process obeys Poisson’s distribution. It is given that the mean of the process is 5. Then the variance of the process is**

- (a) 5
- (b) 0.5
- (c) 25
- (d) 0

**Q.6 Which one of the following gives the average value or expectation of the function g(x) of the random variable X? {Given f(x) is the probability density function}**

(a) E[g(x)] = \int_{-\infty}^{\infty} g(X)dX

(b) E[g(x)] = \int_{-\infty}^{\infty} g(X)f(X)dX

(c) E[g(x)] = \int_{-\infty}^{\infty} g^*(X)dX

(d) E[g(x)] = \int_{-\infty}^{\infty} \left[ \frac{g(X)}{f(X)}\right ]

**Q.7 The auto-correlation function R_X(\tau) of a random process has the property that R_X(0) is equal to **

(a) The square of the mean value of the process

(b) The mean squared value of the process

(c) The smallest value of R_X(\tau)

(d) 1/2 \left[ R_X(\tau) + R_X(-\tau)\right ]

**Q.8 If a linear time-invariant system is excited by a truly random signal like white noise, the output of the linear system will have which of the following properties**

- (a) Output will be a white noise
- (b) Output will be periodic
- (c) Output will not be random
- (d) Output will be correlated or colored noise

**Q.9 Which of the following is/are not a property/properties of a power spectral density function S_X(w)?**

- (a) S_X(w) is a real function of w
- (b) S_X(w) is an even function of w
- (c) S_X(w) is a non-positive function of w. i.e. S_X(w) \leq 0 for all w
- (d) All of the above

**Q.10 What is the spectral density of white noise?**

- (a) A constant
- (b) \delta(w)
- (c) [\delta(w)]^2
- (d) A step function in w

**Q.11 Let x(n) be a real-valued sequence that is a sample sequence of a wide-sense stationary discrete-time random process. The power density function of this signal is**

- (a) real, odd, and non-negative
- (b) real, even, and non-negative
- (c) purely imaginary, even, and negative
- (d) purely imaginary, odd, and negative

**Q.12 Which one of the following is the correct statement? if the value of the resistor creating thermal noise is doubled, the noise generated is**

- (a) halved
- (b) doubled
- (c) unchanged
- (d) slightly changed

**Q.13 The output of two noise sources each producing uniformly distributed noise over the range -a to +a are added. What is the p.d.f. of the added noise?**

- (a) Uniformly distributed over the range -2a to +2a
- (b) Triangular over the range -2a to +2a
- (c) Gaussian over the range -\infty to \infty
- (d) None of the above

**Q.14 If random process x(t) and y(t) are orthogonal then, statistical averages**

- (a) and time averages are different
- (b) and time averages are the same
- (c) are greater than time averages
- (d) are smaller than time averages

**Q.15 The spectral density and autocorrelation function of white noise is**

- (a) Delta and uniform
- (b) Uniform and delta
- (c) Gaussian and uniform
- (d) gaussian and delta

**Q.16 The probability cumulative distribution function must be monotone and**

- (a) increasing
- (b) decreasing
- (c) non-increasing
- (d) non-decreasing

**Q.17 For a random signal (continuous time) x(t) defined for t >0, its probability density function (pdf) at t=t _{0} is such that**

- (a) It is non-negative and its integral equals 1
- (b) Need not be non-negative, but integral equal 1
- (c) It is non-negative, but the integral is not 1
- (d) Non of the above

**Q.18 The noise factor of an attenuator pad that has an insertion loss of 6 dB is**

- (a) 0.25
- (b) 0.5
- (c) 2
- (d) 4

**Q.19 The cumulative distribution function of a random variable x is the probability that X takes the value.**

- (a) less than or equal to x
- (b) equal to x
- (c) greater than x
- (d) Zero

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