Interval of distribution changes

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Let the random variable Θ be uniformly distributed in the interval [0,2π] Suppose we have X=Cos(Θ) and Y=Sin(Θ) . Analyze the distribution to find whether the random variables X and Y are independent? Are they uncorrelated? Are they orthogonal?

Comment on the uncorrelatedness if the interval of distribution changes to [0,π/2]

Reference no: EM132518809

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