hw3-sol

# hw3-sol - AMS 311 (Fall, 2009) Joe Mitchell PROBABILITY...

This preview shows pages 1–2. Sign up to view the full content.

AMS 311 (Fall, 2009) Joe Mitchell PROBABILITY THEORY Homework Set # 3 – Solution Notes (1). (30 points) Aboxcon ta ins10d imes ,15n icke ls ,and4penn ies .Wedraw2coins at random (without replacement). Let X represent the amount (in cents) that we draw out of the box. (a). Give (explicitly) the probability mass function for X .A l soshowap lo to fi t . By considering each possible outcome, we see that the possible values for X are { 2 , 6 , 10 , 11 , 15 , 20 } . The probability function is given by p ( x )= P ( X = x )= ( 4 2 ) ( 29 2 ) if x =2 ( 4 1 )( 15 1 ) ( 29 2 ) if x =6 ( 15 2 ) ( 29 2 ) if x =10 ( 4 1 )( 10 1 ) ( 29 2 ) if x =11 ( 15 1 )( 10 1 ) ( 29 2 ) if x =15 ( 10 2 ) ( 29 2 ) if x =20 0 otherwise The plot of p ( x ) simply consists of “spikes” of the appropriate heights at x =2 , 6 , 10 , 11 , 15 , 20, with p ( x ) = 0 everywhere else. (b). Give (explicitly) the cdf, F ( x ) ,for X .A l soshowap lo to fi t . The cdf is a staircase with step heights given by the spike heights of the pmf: F ( x )= P ( X x )= 0 if x< 2 ( 4 2 ) ( 29 2 ) if 2 x< 6 ( 4 2 ) ( 29 2 ) + ( 4 1 )( 15 1 ) ( 29 2 ) if 6 x< 10 ( 4 2 ) ( 29 2 ) + ( 4 1 )( 15 1 ) ( 29 2 ) + ( 15 2 ) ( 29 2 ) if 10 x< 11 ( 4 2 ) ( 29 2 ) + ( 4 1 )( 15 1 ) ( 29 2 ) + ( 15 2 ) ( 29 2 ) + ( 4 1 )( 10 1 ) ( 29 2 ) if 11 x< 15 ( 4 2 ) ( 29 2 ) + ( 4 1 )(

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## hw3-sol - AMS 311 (Fall, 2009) Joe Mitchell PROBABILITY...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online