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sample-f04 - Stat 126 Final Exam Fall 2004 Name ID I pledge...

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Stat 126 Final Exam Fall 2004 Name: ID#: I pledge that I have neither given nor received unauthorized aid on this exam. Signature: (1) Check “true” or “false”. (1.1) If X Exp ( λ ), Y Exp ( μ ), and P ( X 1) < P ( Y 1), then λ < μ . true ; false . (1.2) If X Geom ( p 1 ), Y Geom ( p 2 ), and P ( X > 1) > P ( Y > 1), then p 1 > p 2 . true ; false . (1.3) If X Uniform ( - 1 , 1), Y Uniform ( - c, c ), and V arY = 2 V arX , then c = 2. true ; false . (1.4) If X and Y are iid with X Poisson (1), then 2 X + Y Poisson (3). true ; false . (1.5) If X and Y are iid with X Poisson (1), then V ar (2 X - Y ) = 5. true ; false . (1.6) If X and Y are iid with X N (0 , σ 2 ), then 4 X - 3 Y and 5 Y have the same distribution. true ; false . (1.7) If X and Y are iid with X N (0 , 1), then E £ ( X - Y ) 2 / = 4. true ; false . (1.8) Let X and Y denote the total numbers of heads and tails among 5 tosses of a coin ( p ) with p < 1 / 2, then P ( X > 2) > P ( Y > 2). true ; false . 1
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(1.9) Let X and Y denote the total numbers of heads and tails among 5 tosses of a coin ( p ), then corr ( X, Y ) = - 1. true ; false . (1.10) If ( X 1 , X 2 ) and ( Y 1 , Y 2 ) have the same distribution, then Cov ( X 1 , X 2 ) = Cov ( Y 1 , Y 2 ). true ; false . (1.11) If ( X 1 , X 2 ) and ( Y 1 , Y 2 ) have the same distribution, then EX 1 = EY 1 . true ; false . (1.12) If the indicators I A , I B satisfy I A I B = 1, then the events A and B are independent.
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