Fourier Transfer and a game?!?!

• To: mathgroup at smc.vnet.net
• Subject: [mg54106] Fourier Transfer and a game?!?!
• From: "elparedblanco" <cire1611 at gmail.com>
• Date: Thu, 10 Feb 2005 02:47:56 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```let's say we have a probabability of picking an amount of money from a
vat.  I can go into the vat either 0,1,2,3 times.  The probability with
which I pick from the vat is described by the vector {.4, .35,.15,.1}.
I call this frequency.

I can pull only four amounts of money from the vat.  The amounts are
{\$2500,\$5000,\$7500,\$10000}.  The probability of picking each amount is
described by the vector {.35,.35,.15,.15}. I call this severity1.

Process is this.  First I choose how many times I can go into the vat.
Then I go in that many times.  I always replace what I pick out.  so it
is possible to win \$30000.

The Question is what's the probabililty of winning certain amounts of
money, such as 15,000 or 7,500 or any number, given the fact that I can
pick multiple times?

Below is the CODE and the ANSWER...I'm close, but close don't cut it.
I think it has something to do with setting the Fourier Parameters.

CODE:

In[149]:=
severity1={.35,.35,.15,.15,0,0,0,0,0,0,0,0,0,0,0,0}

In[150]:=
Length[severity1]

In[151]:=
lossList={2500,5000,7500,10000,0,0,0,0,0,0,0,0,0,0,0,0}

In[161]:=
freq={.4,.35,.15,.1,0,0,0,0,0,0,0,0,0,0,0,0,0}

In[153]:=
fftSeverity = Fourier[severity1]

In[154]:=
one = fftSeverity*Sqrt[1]*.35

In[155]:=
two = fftSeverity^2*Sqrt[1]*.15

In[156]:=
three = fftSeverity^3*Sqrt[1]*.1

In[157]:=
totalFourier = one + two + three

In[158]:=
finalDistribution = InverseFourier[totalFourier]

In[159]:=
Total[finalDistribution]

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