Question: the question is as below: Let X and Y be two independent and identically distributed standard normal random variables. Let 0 c [0, 27), U

the question is as below:

Let X and Y be two independent and identically distributed standard normal random variables. Let 0 c [0, 27), U and V be two random variables such that: U = X cos 0 - Y sin 0 V = X sin 0 + Y cos 0 Show that the joint probability density function of (U, V ) is fu (u, v) = 1 2 TT expl- ( 2 2 + 02 ) ]

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