** Using WeBWorK **

DOCUMENT();      

loadMacros(

   "PGstandard.pl",     # Standard macros for PG language

   "MathObjects.pl",

   #"source.pl",        # allows code to be displayed on certain sites.

   #"PGcourse.pl",      # Customization file for the course

);

# Print problem number and point value (weight) for the problem

TEXT(beginproblem());

# Show which answers are correct and which ones are incorrect

$showPartialCorrectAnswers = 1;

##############################################################

#

#  Setup

#

#

Context("Numeric");

#$k=random(0,2); #pick negative binomial, Binomial,, or Poisson

$k=0;

if ($k==0) #negative binomial

{$r=random(1,7);

$beta=list_random(1,3,4,.25);

#$beta=.25,$r=3;

$a=$beta/(1+$beta);

$b=($r-1)*$a;

$c1=$a+$b;

$c2=$a+$b/2;

$c3=(-$r)*(ln(1+$beta));

$ans=exp(($c3));}

if ($k==1) #Poisson

{$c1=random(.1,.9,.1); #this is lambda; it's also b

$c2=$c1/2;

$ans=exp(-$c1);}

if ($k==2) #Binomial

{$q=list_random(.2,.5,.6,.8);

$m=random(2,5);

$a=-$q/(1-$q);

$b=-($m+1)*$a;

$c1=$a+$b;

$c2=$a+$b/2;

$ans=(1-$q)**$m;};

##############################################################

#

#  Text

#

#

Context()->texStrings;

BEGIN_TEXT

For a distribution in the \((a,b,0)\) class, you are given that \(p_1=$c1 p_0\) and \(p_2=$c2 p_1\).

$BR

Determine \(p_0\).

$BR

answer=\{ans_rule\}

END_TEXT

Context()->normalStrings;

##############################################################

#

#  Answers

#

#

ANS(Compute($ans)->cmp);

# relative tolerance --3.1412 is incorrect but 3.1413 is correct

# default tolerance is .01 or one percent.