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Unformatted text preview: EECS 501 EXAM #1 Fall 2001 PRINT YOUR NAME HERE: HONOR CODE PLEDGE: I have neither given nor received aid on this exam, nor have I concealed any violations of the honor code. Open book; SHOW ALL OF YOUR WORK! SIGN YOUR NAME HERE: (40) 1. Random variables x,y have joint pdf f x,y ( X,Y ) = n cXY if 0 < Y < X < 1 otherwise where c is a constant. Random variable z = y/x . (05) a. Compute the constant c in the pdf f x,y ( X,Y ). (05) b. Are x and y independent? Explain your answer. (05) c. Compute the marginal pdf f x ( X ). (05) d. Compute the conditional pdf f y | x ( Y | X ) at X = 1 / 2. (10) e. Compute the pdf f z ( Z ) using the method of events . (10) f. Compute Pr [( x + y ) < 1]. Hint: inner integral over y . NOTE: Half-credit if you do this problem with cXY replaced with c in f x,y ( X,Y ). WRITE YOUR ANSWERS HERE. SIMPLIFY TO A FRACTION. (a): (c): (e): (b): (d): (f): (40) 2. We flip coin A, which has Pr[heads]=2/3. All flips are independent....
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This note was uploaded on 07/22/2011 for the course EECS 370 taught by Professor Lehman during the Spring '10 term at University of Florida.
- Spring '10