[rochester] / trunk / rochester_problib / setProbability9PoissonDist / ur_pb_9_1.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

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

Mon Jun 25 19:20:51 2001 UTC (11 years, 10 months ago) by sam
File size: 1490 byte(s)
added problem library as webwork/ww_prob_lib with revision tag prob-lib-2


    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
9 "PG.pl",
10 "PGbasicmacros.pl",
11 "PGchoicemacros.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.