I let the random variable r represent the amplitude of, Basic Statistics

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I let the random variable r represent the amplitude of

The random variable X represents the amplitude of a sine wave; Y represents the amplitude of a cosine wave. Both are independently and uniformly distributed over the interval 0 to 1.

(i) Let the random variable R represent the amplitude of their resultant; that is, R² = X² + y². Find and sketch the probability density function of R.

(ii) Let the random variable 0 represent the phase angle of the resultant; that is, θ = tan^-1 (Y/X). Find and sketch the probability density function of θ.

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