The random variables x and θ are independent and θ is uniform in the interval (-π, π). Show that if z = x cos(w t + θ), then

Question

The random variables x and θ are independent and θ is uniform in the interval (-π, π).
Show that if z = x cos(w t + θ), then
                      -|z|                                                  ∞
fz(z) = (1/π) ∫        {fx(y) / √(y² - z²)}dy + (1/π) ∫      {fx(y) / √(y² - z²)}dy
                      -∞                                                   |z|

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