Question

Let Θ ∼ Unif.([0, 2π]) and consider X = cos(Θ) and Y = sin(Θ).

Can you find E[X], E[Y], and E[XY]?

clearly, x and y are not independent

I think E[X] = E[Y] = 0 but how do you find E[XY]?

Answer #2

similarly E(Y) = 0

XY = sin *cos

period of sin = 2 pi , sin 2 = pi , hence integral is 0

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answered by: anonymous

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