assn6 - (a) Compute E [ X 3 ] (b) Show that Y = X 3 has a...

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Math 361, Problem set 6 Due 10/18/10 1. (1.8.3) Let X have pdf f ( x + 2) / 18 for - 2 < x < 4, zero elsewhere. Find E [ X ] , E [( X + 2) 3 ] and E [6 X - 2( X + 2) 3 ]. 2. (1.8.5) Let X be a number selected uniformly random from a set of num- bers { 51 ,..., 100 } . Approximate E [1 /X ]. Hint: Find reasonable upper and loewr bounds by finding integrals bounding E [1 /X ] . 3. Let X have the pdf f ( x ) = 1 /x 3 . Find E [ X ], but show that e [ X 2 ] does not exist. 4. (1.8.14) Let X have the pdf f ( x ) = 3 x 2 , 0 < x < 1, zero elsewhere.
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Unformatted text preview: (a) Compute E [ X 3 ] (b) Show that Y = X 3 has a uniform(0,1) distribution. (c) Compute E [ Y ] and compate this result with the answer obtained in Part (a). 5. (1.9.4) If the E [ X 2 ] exists, show that E [ X 2 ] ≥ ( E [ X ]) 2 6. (1.9.8) Let X be a random variable such that E [( X-b )] exists for all real b . Show that E [( X-b ) 2 ] is minimized when b = E [ X ]. 1...
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This note was uploaded on 10/26/2010 for the course MATHCS Math 316 taught by Professor Dr.paulhorn during the Fall '10 term at Emory.

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