Let X and Y be independent Gaussian(0,1) random variables. Define the random variables R and Θ,...

Let X and Y be independent Gaussian(0,1) random variables. Define the random variables R and Θ, by R2=X2+Y2,Θ = tan−1(Y/X).You can think of X and Y as the real and the imaginary part of a signal. Similarly, R2 is its power, Θ is the phase, and R is the magnitude of that signal.

(b) Find the probability density functions of R and Θ. Are R and Θ independent random variables?

Expert Solution

TOPIC:Transformation of random variables.

orchestra answered 1 year ago

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