文档介绍：For Students
Solutions to Odd-Numbered End-of-Chapter Exercises
Chapter 2
Review of Probability
. (a) Probability distribution function for Y
e (number of heads) Y  0 Y  1 Y  2
Probability
(b) Cumulative probability distribution function for Y
e (number of heads) Y  0 0  Y  1 1  Y  2 Y  2
Probability 0
d
(c) Y = EY( )(0 ) (1 ) (2 )  . FFq,.
Using Key Concept : var(YEYEY )(22 ) [ ( )] ,
and
(|uXii )
so that
var(YEYEY )(22 ) [ ( )]  () 2 .
. For the two new random variables WX 36 and VY 20 7 , we have:
(a) EV( ) E (20 7 Y ) 20 7 EY ( ) 20 7 0 78 14 54,
EW() E (36)36()3607072 X  E X 
222
(b) WXvar (3 6X ) 6 36 0 21 7 56,
222
VYvar (20 7Y ) ( 7) 49 0 1716 8 4084
(c) WV cov(3  6XY , 20  7 )  6 (  7)cov( XY , )  42  0  084  3  528
3528
corr (WV , )WV  0 4425
WV 7 56 8 4084
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Solutions to Odd-Numbered End-of-Chapter Exercises 3
. Let X denote temperature in F and Y denote temperature in C. Recall that Y  0 when X  32 and
Y 100 when X  212; this implies YXYX(100/180)( 32) or  (5/9) . Using Key
o o
Concept , X  70 F implies that Y  (5/9) 70 C, and X  7 F implies
 Y (5/9) 7 C.
22 2
. Using obvious notation, CMF; thus CMF and CMF2cov(M ,F ). This
implies
(a) C 40 45 $85,000 per year.
cov(M ,F )
(b) corr (MF , ) , so that cov(M ,FMF ) MF corr ( , ). Thus cov(MF , ) 
MF
12 18  , where the units are squared thousands of dollars per year.
22 2 222
(c) CMF2cov(M ,F ), so that C 12 18 2  , and
 C  thousand dollars per year.
(d) First you need to look up the current Euro/dollar exchange rate in the Wall Street