Unformatted text preview: X, Y ) can be described in polar coordinates in terms of random variables R ≥ 0 and Θ ∈ [0 , 2 π ], so that X = R cosΘ , Y = R sinΘ . Show that R and Θ are independent (i.e. show f R, Θ ( r, θ ) = f R ( r ) f Θ ( θ )). (a) Find f R ( r ). (b) Find f Θ ( θ ). (c) Find f R, Θ ( r, θ ). 4. Problem 4.20, page 250 in text. Schwarz inequality . Show that for any random variables X and Y , we have ( E [ XY ]) 2 ≤ E [ X 2 ] E [ Y 2 ] . Page 1 of 1...
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 Spring '11
 Proasin
 Computer Science, Electrical Engineering, Probability theory, Massachusetts Institute of Technology, CDF, Probabilistic Systems Analysis, Department of Electrical Engineering & Computer Science

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