View of /trunk/NationalProblemLibrary/UVA-Stat/setStat212-Homework06/stat212-HW06-17.pg

    1 ## DESCRIPTION
    2 ##  Statistics: Probability
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('statistics', 'probability')
    6 ## naw tagged this problem.
    7 
    8 ## DBchapter('Continuous Probability Distributions')
    9 ## DBsection()
   10 ## Date('6/27/2005')
   11 ## Author('Jeff Holt')
   12 ## Institution('UVA')
   13 ## TitleText1('Statistics for Management and Economics')
   14 ## EditionText1('6')
   15 ## AuthorText1('Keller, Warrack')
   16 ## Section1()
   17 ## Problem1()
   18 
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGnumericalmacros.pl",
   28 "PGstatisticsmacros.pl",
   29 "PGauxiliaryFunctions.pl"
   30 );
   31 
   32 TEXT(beginproblem());
   33 $showPartialCorrectAnswers = 1;
   34 ## install_problem_grader(~~&std_problem_grader);
   35 
   36 $ans1 = 0;
   37 $ans2 = 0;
   38 $ans3 = 0;
   39 $ans4 = 0;
   40 while (($ans1 < 0.002) || ($ans2 < 0.002) || ($ans3 < 0.002) || ($ans4 < 0.002)) {
   41 $lambda = random(.25,.75,0.02);
   42 $a1 = $lambda - random(.05,.2,0.01);
   43 $a2 = $lambda - random(.05,.2,0.01);
   44 $b2 = 5*$lambda + random(.05,.2,0.01);
   45 $ans1 = exp(-$lambda);
   46 $ans2 = exp(-$a1*$lambda);
   47 $ans3 = 1 - exp(-$lambda*$lambda);
   48 $ans4 = exp(-$a2*$lambda) - exp(-$b2*$lambda);
   49 }
   50 
   51 BEGIN_TEXT
   52 $PAR
   53 Suppose that \(X\) is an exponentially distributed random variable
   54 with \(\lambda = $lambda\).  Find each of the following probabilities:
   55 
   56 $PAR
   57 A. \(P(X > 1)\) = \{ans_rule(15)\}
   58 
   59 $PAR
   60 B. \(P(X > $a1)\) = \{ans_rule(15)\}
   61 
   62 $PAR
   63 C. \(P(X < $lambda)\) = \{ans_rule(15)\}
   64 
   65 $PAR
   66 D. \(P($a2 < X < $b2)\) = \{ans_rule(15)\}
   67 
   68 END_TEXT
   69 
   70 ANS(num_cmp($ans1));
   71 
   72 ANS(num_cmp($ans2));
   73 
   74 ANS(num_cmp($ans3));
   75 
   76 ANS(num_cmp($ans4));
   77 
   78 
   79 ENDDOCUMENT();       # This should be the last executable line in the problem.