410Hw01 - STAT 410 U3, G4 Fall 2011 Homework #1 (due...

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STAT 410 – U3, G4 Fall 2011 Homework #1 (due Friday, September2, by 3:00 p.m.) 1. Below is a list of moment-generating functions. Provide (i) the values for mean μ and variance σ 2 , and (ii) P ( 1 X 2 ) for the random variable associated with each moment-generating function. ( Justify your answers. ) a) M X ( t ) = 5 7 . 0 0.3 + t e . b) M X ( t ) = ( ) 1 3 - t e e . c) M X ( t ) = 2 25 . 0 1 75 . 0 - t t e e , t < ln 4. d) M X ( t ) = e 5 t . 2. Below is a list of moment-generating functions. Provide (i) the values for mean μ and variance σ 2 , and (ii) P ( 1 X 2 ) for the random variable associated with each moment-generating function. ( Justify your answers. ) a) M X ( t ) = 3 25 . 0 1 1 - t , t < 4. b) M X ( t ) = e t ( 3 + 2 t ) . c) M X ( t ) = t t e 5 1 5 - , t 0, M X ( 0 ) = 1.
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3. Suppose a discrete random variable X has the following probability distribution:
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This note was uploaded on 10/31/2011 for the course MATH 464 taught by Professor Monrad during the Fall '08 term at University of Illinois, Urbana Champaign.

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410Hw01 - STAT 410 U3, G4 Fall 2011 Homework #1 (due...

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