a2su112131

# a2su112131 - Balls are drawn from the box without...

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MATH 2131 3.00 MS2 Assignment 2 Total marks = 40 Question 1: Let X 1 ,X 2 ,...,X 6 be a random sample on X where f X ( x ) = ( 1 /x 2 , x 1 , 0 , otherwise. (a) (5 marks). Find the pdf of X (6) . (b) (5 marks). Find the pdf of X (3) . Question 2: Let ( X,Y ) have the joint pdf f X,Y ( x,y ) = ( xy/ 2 , 0 < x < y < 2 , 0 , otherwise. (a) (5 marks). Find the joint pdf for U = X/Y and V = Y . (b) (2 marks). Are U and V independent? Why? (c) (4 marks). Find f U ( u ) and f V ( v ). Question 3: (10 marks). Let X Uniform[0,1] and Y Uniform[0,2], where X and Y are independent. Find the pdf of Z = X + Y . Question 4: (4 marks). A box contains 6 white balls and 4 black balls.

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Unformatted text preview: Balls are drawn from the box without replacement until either a white ball is drawn or 3 balls have been drawn. Find the expected number of balls that will be drawn from the box. Question 5: (a) (3 marks). Let r.v. X have pdf f X ( x ) = e-| x | / 2 ,-∞ < x < ∞ . Find E ( X ). 1 (b) (2 marks). Let r.v. X have pdf f X ( x ) = ( 1 /x 2 , x ≥ 1 , , otherwise. Find E ( X ). 2...
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a2su112131 - Balls are drawn from the box without...

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