Communications ...

The number of cars arriving at ICICI bank drive-in window during 10-min period is Poisson random variable X with b = 2.

When a carrier signal is amplitude modulated by a sinusoidal signal, the antenna current of the transmitter is increased by 20% from that of an unmodulated case. The modulation index of the AM signal is equal to_______. (Correct up to three decimal places)

A speech signal is sampled at 8 kHz compressed and encoded into 8-bits/sample. The PCM data is 8 QAM modulated and transmitted through an AWGN based cosine filter having roll-off factor 0.2 is used, then required bandwidth for transmission is:

Delhi averages three murder per week and their occurrences follow a poission distribution

The probability that there will be five or more murder in a given week is

The random variable X is defined by the density

The expected value of g(X) = X³ is

The random variables X and Y have variances 0.2 and 0.5 respectively. Let Z= 5X-2Y. The variance of Z is?

Let (𝑡) be a wide sense stationary (WSS) random process with power spectral density 𝑆_𝑋(𝑓). If Y(t) is the process defined as 𝑌(𝑡) = 𝑋(2𝑡 − 1), the power spectral density 𝑆_𝑌(𝑓) is

The variance of the random variable X with probability density function  is

An on-off Baseband signal is transmitted and the probability of error was found to be \({P_{e1}} = Q\left( {\sqrt k } \right).\) The same signal was ASK modulated and the probability of error was \({P_{{e_2}}} = Q\left( {\sqrt {zk} } \right).\) The z = _____

(Assume Amplitude of carrier in ASK = Maximum amplitude of on-off signal)

The Bandwidth of a TV video plus audio signal is 4.5 MHz. If this signal is converted into PCM bit stream with 1024 quantization levels, the bitrate of the resulting signal will be:

Let x be a continuous Random variable with PDF

\(f_{x}(x)=\frac{3}{x^4}\), for x ≥ 1

A source generates 4 symbols with probabilities P(x₁) = 0.4, P(x₂) = 0.3, P(x₃) = 0.2 and P(x₄) = 0.1. Find the amount of information contained in the message x₁ x₂ x₁ x₃

Consider a random process Z(t) = 2X(t) + 3Y(t), where X(t) and Y(t) are mutually orthogonal stationary random processes with zero mean and autocorrelation functions \({R_{XX}}\left( \tau \right) = 5{e^{ - 2\tau }}\) and \({R_{YY}}\left( \tau \right) = 3\tau + 7\), respectively. The power in Z(t) is:

A Random variable X is uniformly distributed on the interval (-5, 15). Another random variableY = e ^-X/5 is formed. The value of E[Y ] is

An AM signal is represented by:

x(t) = (20 + 4 sin 500 πt) cos (2π × 10⁵ t) V

which of the following conclusion is/are correct?

A joint sample space for two random variable X and Y has four elements (1, 1), (2, 2), (3, 3) and (4, 4). Probabilities of these elements are 0.1, 0.35, 0.05 and 0.5 respectively.

The probability of the event {X ≤ 2.5, Y ≤ 6} is

In a system, voice signals with maximum frequency component of 3.5 kHz are sampled at twice the Nyquist rate. The sampled signal is quantized into levels that produce N symbols {s₀, s₁, s₂, … , s_N-2, s_N-1}. These symbols occur independently with probabilities:

\(\frac{1}{2},\;\frac{1}{4},\frac{1}{8}, \ldots ,\frac{1}{{{2^{N - 1}}}},\frac{1}{{{2^{N - 1}}}}\).

Two random variable X and Y have the density function

The X and Y are

The value of σx², σy², RXY and ρ are respectively

The mean value of the random variable

W = (X + 3Y)² + 2X + 3 is

A (7, 4) block code has a generator matrix as shown.

\(G = \left[ {\begin{array}{*{20}{c}}1&0&0&0&1&1&0\\0&1&0&0&0&1&1\\0&0&1&0&1&1&{1}\\0&0&0&1&1&0&1\end{array}} \right]\)

A superheterodyne receiver is to operate in the frequency range 550 kHz – 1650 kHz, with an intermediate frequency of 450 kHz. Let r = C_max/C_min denote the required capacitance ratio of the local oscillator and f’_c denote the image frequency (in kHz) of the incoming signal.

A CRT Terminal is used to enter alphanumeric data into a computer. The CRT is connected to the computer through a voice grade telephone line having a usable bandwidth of 3000 Hz and output \(\frac{S}{N}\) of 10dB. Assume that the terminal has 128 characters and the data sent from the terminal consists of independent sequence of equiprobabe characters maximum rate at which data can be transmitted from terminal to computer without errors.

If machine is not properly adjusted, the product resistance change to the case where ax = 1050Ω. Now the rejected fraction is

A The power spectrum of a random noise X(t) is defined as:

\({S_X}\left( \omega \right) = \frac{3}{{49 + {\omega ^2}}}\)

This is applied to a differentiator that has a transfer function H(ω) = jω. The output is then applied to a network for which h(t) = t² e^-7t u(t).