Re: BinomialDistribution
- To: mathgroup at smc.vnet.net
- Subject: [mg65226] Re: BinomialDistribution
- From: Bill Rowe <readnewsciv at earthlink.net>
- Date: Sun, 19 Mar 2006 03:19:03 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
On 3/18/06 at 6:40 AM, J.A.Solomon at city.ac.uk (Solomon, Joshua)
wrote:
>This makes me feel foolish.
>In[1]:=Needs["Statistics`DiscreteDistributions`"]
>In[2]:=Plot[PDF[BinomialDistribution[101,u],26],{u,0,0.5},PlotRange
>->All]
>This gives me a nice, bell-shaped curve, with a minimum of about 0
>and a maximum of about .09. Let's integrate it from 0 to .29.
>In[3]:=Integrate[PDF[BinomialDistribution[101,u],26],{u,0,.29}]
>Out[3]=-0.612253
>How can this be negative?
The problem is the default precision when Integrate substitutes values for u into the symbolic solution. The simplest solution is to use NIntegrate instead of Integrate, i.e.,
In[12]:=
NIntegrate[PDF[BinomialDistribution[101,u],26],{u,0,.29}]
Out[12]=
0.00731803
Equivalently, you could change the limits for integration to an exact number and convert the answer to a machine precision number using N, i.e,
In[13]:=
Integrate[PDF[BinomialDistribution[101,u],26],{u,0,29/100}]//N
Out[13]=
0.00731803
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