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Application of probabilistic methods for determination of signals

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rupsdbb

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A random signal from a deep-space probe is uniformly distributed between 17.324V and 32.574V.
It is observed in the presence of Gaussian noise N having zero mean and standard deviation of 9V.
If the observed value of the signal plus noise is 19V, find the best estimate of the signal amplitude.

In a stormy sea, the following waves are present:
x1 (l) = 12 cos (ω1 l + θ1 )
x2 (l) = 9 cos (ω2 l + θ2 )
x3 (l) = 7 cos (ω3 l + θ3 )
x4 (l) = 3 cos (ω4 l + θ4 )

The amplitudes of the waves are given in metres. With the relevant wave diagrams to explain, answer the following questions:

i. Under what conditions the highest wave will occur in this storm?
ii. What will be the height of the highest wave in this storm?
iii. Under what conditions only one such wave is possible and under what condition successive such waves are possible?


Somebody please help me solve this two questions. Its driving me crazy :sad:
 

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