Unformatted text preview: working time. 3. [5 + 3 + 2 = 10 pts] A transmitter sends out a signal X ∼ N (1 , 1 / 4). If x is the original signal, then because of some noise the receiver gets a signal Y which is normal with mean a + bx and standard deviation b | x | for some constants a and b such that b > 0. If it is known that E ( Y ) = 0 , var ( Y ) = 3, then (a) ﬁnd a and b , (b) cov ( X, Y ) and (c) correlation coeﬃcient ρ ( X, Y ). 4. [4 + 6 = 10 pts] Suppose that X, Y have joint PDF f X,Y ( x, y ) = ± 8 xy, ≤ x ≤ y ≤ 1 otherwise . (a) Find var ( XY ) and (b) correlation coeﬃcient ρ ( X, XY ). 5. [5 + 5 = 10 pts] If X, Y are independent Uniform (0 , 1) random variables, then ﬁnd the correlation coeﬃcients (a) ρ ( X, X + Y ) and (b) ρ ( X-Y, X + Y ). 1...
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This homework help was uploaded on 02/20/2009 for the course ORIE 3500 taught by Professor Weber during the Fall '08 term at Cornell.
- Fall '08