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Unformatted text preview: Y 2 =sin θX 1 + cos θX 2 have the same joint distribution. In words, this distribution is invariant under rotation. 4. Suppose X 1 , . . . , X n are independent and have density function f ( z ) . Let Y = min ( X 1 , . . . , X n ) and Z = max ( X 1 , . . . , X n ) . Compute P ( Y ≥ y, Z ≤ z ) and diﬀerentiate to ﬁnd the joint density of Y and Z . 5. Suppose X and Y are independent and have density function f ( x ) = 2 x for 0 < x < 1. Find the density function of X + Y. 6. Suppose X and Y are independent and have exponential distributions with λ < μ. Find the density function of X + Y....
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This note was uploaded on 09/22/2010 for the course MATH 413 at Cornell.
 '08
 PROTSAK
 Probability

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