| Original Message (ID '98671') By Bill Simpson: |
| In Response To 'Re: Utility_Function'
---------
Ah, much more helpful.
Here is one way.
In[16]:= w=5.;c=3.;
toss=gain=probability=rewards=changeInWealth=utility=Table[0,{11}];
For[i=1,i≤11,i++,
toss[[i]]=i;
gain[[i]]=2^(toss[[i]]-1);
probability[[i]]=.5^toss[[i]];
rewards[[i]]=If[i==1,gain[[i]]*probability[[i]],gain[[i]]*probability[[i]]+rewards[[i-1]]];
changeInWealth[[i]]=Log[w+gain[[i]]-c]-Log[w];
utility[[i]]=Total[Take[changeInWealth,i]*Take[probability,i]]
];
Transpose[{toss,gain,probability,rewards,changeInWealth,utility}]
Out[20]=
{{1, 1, 0.5, 0.5, -0.5108, -0.2554},
{2, 2, 0.25, 1., -0.2231, -0.3112},
{3, 4, 0.125, 1.5, 0.1823, -0.2884},
{4, 8, 0.0625, 2., 0.6931, -0.2451},
{5, 16, 0.0313, 2.5, 1.2809, -0.2051},
{6, 32, 0.0156, 3., 1.9169, -0.1751},
{7, 64, 0.0078, 3.5, 2.5802, -0.1549},
{8, 128, 0.0039, 4., 3.2581, -0.1422},
{9, 256, 0.0020, 4.5, 3.9435, -0.1345},
{10, 512, 0.0010, 5., 4.6328, -0.1300},
{11, 1024, 0.0005, 5.5, 5.3240, -0.1274}}
There are at least a dozen different ways of doing anything in Mathematica. |
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