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Suppose X and Y are independent and Gaussian with means

Suppose X and Y are independent and Gaussian with means of μX and μY, respectively, and equal variances of σ2. The polar variables are formed according to R =√ X2 + Y2 and θ = tan–1 (Y / X).

- Find the joint PDF of R and θ.

- Show that the marginal PDF of R follows a Rician distribution.

- Find the joint PDF of R and θ.

- Show that the marginal PDF of R follows a Rician distribution.

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