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Let U and V be two independent zero mean Gaussian random variables of variances 1/4 and 1/9 respectively. The probability P(3V ≥ 2U) is
U and V are two independent zero mean and Gaussian.
let z = 3V  2U
U and V are Gaussian then their linear transformation Z is also Gaussian
than E[z] = E[3V  2U]=3E[V]  2E[U]=0
if z is gaussian and zero mean then its probability for greater than zero is 0.5
Option C is the correct answer.
A device has 200 Ω equivalent noise resistance, 300 Ω input resistor, and the bandwidth of the amplifier is 6 MHz. If the operating temperature of the amplifier is 290° K, the noise voltage at the input of a television RF amplifier will be nearly
Concept:
The noise voltage at the input of the RF amplifier is given by:
Where,
Equivalent resistance (R_{eq}) = R_{Noise }+ R_{in}
Boltzmann constant (k) = 1.38 × 10^{23}
T: Operating temperature.
B: Bandwidth of amplifier.
Calculation:
Given Equivalent resistance (R_{eq}) = 200 + 300 = 500 Ω
B = 6 MHz and T = 290 ^{0}K
Putting on the respective values, we get:
V = 6.92 μV
Which method is much better and efficient?
Vector quantization will always equal or exceed the performance of scalar quantization.
Which reduces the dynamic range of quantization noise in PCM?
Adaptive quantizer reduces the dynamic range of quantization noise in PCM and DPCM.
If Gaussian process is a wide sense stationary process then it will also be strict sense stationary process.
Air craft of Jet Airways at Ahmedabad airport arrive according to a Poisson process at a rate of 12 per hour. All aircraft are handled by one air traffic controller. If the controller takes a 2 – minute coffee break, what is the probability that he will miss one or more arriving aircraft?
P (miss/or more aircraft) = 1 – P(miss 0) = 1 – P(0 arrive).
A random process is defined by X(t) + A where A is continuous random variable uniformly distributed on (0,1). The auto correlation function and mean of the process is
E[X(t)X(t + t)] = 1/3 and E[X(t)] = 1/2 respectively.
The auto correlation function of a stationary ergodic random process is shown below.
What is the value of variance?
Here X = 0, y = 0, Rxx(0) = 5, Ryy(0) = 10. The only value that satisfies all the given conditions is 30.
37 docs22 tests

37 docs22 tests
