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Course: STAT 410, Spring 2008
School: UIllinois
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Word Count: 203

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410 STAT Spring 2008 Version B Name (10 points) ANSWERS . Quiz 1 Be sure to show all your work, your partial credit might depend on it. No credit will be given without supporting work. 1. Consider a continuous random variable X with p.d.f. fX( x) = 2 x 21 0 2&lt; x&lt;5 otherwise a) (4) Find the moment-generating function M X ( t ). 5 2 M X ( t ) = E( e t X ) = = = etx 2 2 5 xdx = xet x d x...

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410 STAT Spring 2008 Version B Name (10 points) ANSWERS . Quiz 1 Be sure to show all your work, your partial credit might depend on it. No credit will be given without supporting work. 1. Consider a continuous random variable X with p.d.f. fX( x) = 2 x 21 0 2< x<5 otherwise a) (4) Find the moment-generating function M X ( t ). 5 2 M X ( t ) = E( e t X ) = = = etx 2 2 5 xdx = xet x d x 21 21 2 5 2 2 1 1 xet x - 2 et x 21 t t 10 2 4 2 e 5t - e 5t - e 2t + e 2t , 2 2 21 t 21 t 21 t 21 t t 0. M X ( 0 ) = 1. b) (6) Let Y = 1 X2 . Find the probability distribution of Y. ( That is, either find the c.d.f. of Y, F Y ( y ), y < < , OR find the p.d.f. of Y, f Y ( y ), < y < . ) fX( x) = 2 x 21 0 0 x<2 2 x<5 2< x<5 FX( x ) = x2 -4 21 1 otherwise x5 Y= 1 X2 . 2<x<5 1 1 <y< . 25 4 1 1/2 g( x) = 1 x2 g 1( y ) = y =y dx 1 3 = y /2 dy 2 1 1 <y< . 25 4 f Y ( y ) = f X ( g 1( y ) ) 2 1 /2 1 3 /2 1 2 dx =( y )( y )= y , 21 2 21 dy OR 1 X 2 FY( y ) = P( Y y ) = P( = 1 FX( y ) = P( X 1 y ) = 1 P( X < 1 y ) 1 y ). = 1 y -1 - 4 21 25 - y -1 = , 21 1 1 <y< . 25 4 0 FY( y ) = y< 1 25 25 - y -1 21 1 1 1 y< 25 4 fY( y) = 1 -2 y 21 0 1 1 <x< 25 4 otherwise y 1 4
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UIllinois - STAT - 410
STAT 410 Spring 2008 Version AName(10 points)ANSWERS.Quiz 2Be sure to show all your work, your partial credit might depend on it.No credit will be given without supporting work.Let X and Y have the joint probability density function1.
UIllinois - STAT - 410
STAT 410 Spring 2008 Version BName(10 points)ANSWERS.Quiz 2Be sure to show all your work, your partial credit might depend on it.No credit will be given without supporting work.Let X and Y have the joint probability density function1.
UIllinois - STAT - 410
STAT 410 Spring 2008 Version AName(10 points)ANSWERS.Quiz 3Be sure to show all your work, your partial credit might depend on it.No credit will be given without supporting work.Let X 1 , X 2 , . , X n be a random sample of size n from t
UIllinois - STAT - 410
STAT 410 Spring 2008 Version BName(10 points)ANSWERS.Quiz 3Be sure to show all your work, your partial credit might depend on it.No credit will be given without supporting work.Let X 1 , X 2 , . , X n be a random sample of size n from t
UIllinois - STAT - 410
STAT 410 Spring 2008 Version AName(10 points)ANSWERS.Quiz 4Be sure to show all your work, your partial credit might depend on it.No credit will be given without supporting work.1.Let X 1 , X 2 , . , X n be independent random variables,
UIllinois - STAT - 410
STAT 410 Spring 2008 Version BName(10 points)ANSWERS.Quiz 4Be sure to show all your work, your partial credit might depend on it.No credit will be given without supporting work.1.Let X 1 , X 2 , . , X n be independent random variables,
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UIllinois - CHEM - 444
Chem 444B Homework Set #2 - Solutions DUE: Friday, February 1, 20081) The energy spacing between a ground rotational state and the 1st excited state is 0.05 kJ/mol. Calculate the ratio of the number of particles in the 1st excited state to the numbe
UIllinois - CHEM - 444
Chem 444B Homework Set #3 - Solutions DUE: Friday, February 8, 20081) a) Calculate rot (in cm-1) for the J = 2 level of O2 given r = 0.12074 nm 2 J ( J + 1) mm rot = , I = r 2 , = 1 2 m1 + m2 2I (16.0 g / mol )(16.0 g / mol ) 2 -9 I = ( 0.12074
UIllinois - CHEM - 444
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UIllinois - CHEM - 444
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Chem 444B Homework Set #6 - Solutions DUE: Friday, March 7, 20081) Beginning with dU = TdS - PdV and H = U + PV . a) Derive the expression dH = TdS + VdP There is more than one correct way to approach this problem. Here is one option: dU = TdS - PdV
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