Prof. Alex Suciu       MTH1187-Probability       Winter 2001

Exam 2: Solutions

Problem 1

male=0.55;  female=0.45;  lhmale=0.15;  rhfemale=0.9; 

FemaleIfRightHanded=female*rhfemale/(female*rhfemale+male*(1-lhmale))

Problem 2

n=35;   p=1/50;

N[p*(1-p)^(n-1)]

Problem 3

pdf[t_]:=2*t*Exp[-t^2];   cdf[t_]:=1-Exp[-t^2];

FilledPlot[{pdf[t],cdf[t]},{t,0,3}]

a=1-cdf[1];  {a,N[a]}

Problem 4

n=100;  dist=BinomialDistribution[n,p];

BarChart[Table[PDF[dist,k],{k,0,9}],BarLabels->Range[0,9]]

PDF[dist,3]

1-CDF[dist,1]   (** alternate way **)

Problem 5

FilledPlot[PDF[dist,x],{x,35,60}]

a=CDF[dist,50]-CDF[dist,45]

b=Quantile[dist,0.90]

Problem 6

FilledPlot[PDF[dist,x],{x,40,100}]

below70=N[CDF[dist,70]]

ABcutoff=Quantile[dist,0.86]

BCcutoff=Quantile[dist,0.6]

CDcutoff=Quantile[dist,0.3]

DFcutoff=Quantile[dist,0.1]

Converted by Mathematica      February 14, 2001