Let theta ~ Unif([0, 2pi]) and consider X = cos(theta) and Y = sin(theta) . (i)...

Question

Question

Let theta ~ Unif([0, 2pi]) and consider X = cos(theta) and Y = sin(theta) .

(i) Determine the correlation coefficient between X and Y .

(ii) Prove that X and Y are not independent.

math Statistics-And-Probability

Answer 1

Answer #1

Giwn that, p~ U(0,2) 2M also, X Cos e Y= Sin Co. (x,Y ) = COVCXN) V C VCY 27T sin (a) ECy) EC Cos OJ = f Cose do LIT 271 27T

Answer 2

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