View of /trunk/rochester_problib/setProbability9PoissonDist/ur_pb_9_1.pg

    1 ##DESCRIPTION
    2 ##KEYWORDS('probability','poisson random variable', 'probability dist')
    3 ##
    4 ##ENDDESCRIPTION
    5 
    6 DOCUMENT();        # This should be the first executable line in the problem.
    7 
    8 loadMacros(
    9 "PG.pl",
   10 "PGbasicmacros.pl",
   11 "PGchoicemacros.pl",
   12 "PGanswermacros.pl",
   13 "PGauxiliaryFunctions.pl"
   14 );
   15 
   16 TEXT(beginproblem());
   17 $showPartialCorrectAnswers = 1;
   18 
   19 for ($i=0; $i<4; $i++) {
   20   $x[$i] = random(1,9,1);
   21   $m[$i] = random(.5,6,.5);
   22 }
   23 $ans0 = ($m[0]**$x[0])*$E**(-$m[0])/fact($x[0]);
   24 
   25 for ($i=0; $i<4; $i++) {
   26   for ($j=0; $j<($x[$i]+1); $j++) {
   27   $prob[$i][$j] = ($m[$i]**$j)/$E**($m[$i])/fact($j);
   28 
   29 }
   30 }
   31 
   32 $sum1 = 0;
   33 for ($j=0; $j<($x[1]+1); $j+=1){
   34   $sum1 = $sum1+$prob[1][$j];
   35 }
   36 
   37 $sum2 = 0;
   38 for ($j=0; $j<($x[2]+1); $j+=1){
   39   $sum2 = $sum2+$prob[2][$j];
   40   $ans2 = 1-$sum2;
   41 }
   42 $sum3 = 0;
   43 for ($j=0; $j<$x[3]; $j+=1){
   44   $sum3 = $sum3+$prob[3][$j];
   45 }
   46 
   47 BEGIN_TEXT
   48 Given that \(x\) is a random variable having a Poisson distribution, compute the following: $PAR
   49 (a) \( \) \( P(x = $x[0])\) when \(\mu = $m[0] \) $BR
   50 \(P(x) = \) \{ans_rule(10)\} $PAR
   51 (b) \( \) \( P(x \leq $x[1]) \)when \(\mu = $m[1] \) $BR
   52 \(P(x) = \) \{ans_rule(10)\} $PAR
   53 (c) \( \) \( P(x > $x[2])\) when \(\mu = $m[2] \) $BR
   54 \(P(x) = \) \{ans_rule(10)\} $PAR
   55 (d) \( \) \( P(x < $x[3])\) when \(\mu = $m[3] \) $BR
   56 \(P(x) = \) \{ans_rule(10)\}
   57 END_TEXT
   58 ANS(num_cmp($ans0));
   59 ANS(num_cmp($sum1));
   60 ANS(num_cmp($ans2, tol=>0.000001));
   61 ANS(num_cmp($sum3));
   62 
   63 ENDDOCUMENT();       # This should be the last executable line in the problem.