ST301
Homework6Solutions
Ch4.4
59.)µX=0(0.01)+1(0.05)+2(0.30)+3(0.43)+4(0.21)=2.78
60.)LetX=#ofnonworderrorsina250‐wordessay,Y=#ofworderrorsina250‐wordessay.
Meannumberofnonworderrors:µX=0(0.1)+1(0.2)+2(0.3)+3(0.3)+4(0.1)=2.1
Meannumberofworderrors:µY=0(0.4)+1(0.3)+2(0.2)+3(0.1)=1
64.)(a)XandYIndependent:µX+Y=µX+µY=2.1+1=3.1
σX+Y=
=
=(0–2.1)2(0.1)+(1–2.1)2(0.2)+(2–2.1)2(0.3)+(3–2.1)2(0.3)+(4–2.1)2(0.1)=1.29
1.291
=(0–1)2(0.4)+(1–1)2(0.3)+(2–1)2(0.2)+(3–1)2(0.1)=1
SoσX+Y=√ .
(b)XandYDependentwithρ=0.5:µX+YisstillµX+µY=2.1+1=3.1
σX+Y=
2
1.29120.51.13581 .
65.)(a)
StockValueafterTwoDays(rise/rise,rise/fall,fall/rise,fall/fall)
Value1.32*2*1000=$562.501000=$16901.3*.75*1000=$975 .75*1.3*1000=$975 .75
Probability0.250.250.250.25
P(stockworthmorethan$1000aftertwodays)=0.25
(b)MeanValue=1690(0.25)+975(0.5)+562.5(0.25)=$1050.625
