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{"sheet":"Cover","index":0,"n_rows":16,"n_cols":7,"rows_kept":16,"cut":false,"hidden":false,"merged":[[12,5,12,6],[13,5,13,6],[14,5,14,6],[15,5,15,6],[4,6,7,10]]}
[]
[]
[]
[]
[null,null,null,null,null,null,"Basic Simulations in Excel"]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,"Hubbard Decision Research"]
[null,null,null,null,null,"2S410 Canterbury Ct"]
[null,null,null,null,null,"Glen Ellyn, IL 60137"]
[null,null,null,null,null,"www.hubbardresearch.com"]

{"sheet":"Deterministic Cash Flow","index":1,"n_rows":16,"n_cols":7,"rows_kept":16,"cut":false,"hidden":false,"merged":[[15,1,16,1],[15,2,16,2]]}
["Deterministic Cash Flow Example"]
[]
[null,"Input Variables",null,"Point Est."]
[null,"Percent reduction in labor cost",null,0.03]
[null,"Current total labor cost",null,75000000]
[null,"Initial development costs (2020)",null,5000000]
[null,"Cost of money",null,6.5000000000000002E-2]
[]
[null,"Cash Flow"]
[null,null,2020,2021,2022,2023,2024]
[null,"Total costs",{"$f":"D6","v":5000000}]
[null,"Total benefits",null,{"$f":"$D5*$D4","v":2250000},{"$f":"$D5*$D4","v":2250000},{"$f":"$D5*$D4","v":2250000},{"$f":"$D5*$D4","v":2250000}]
[null,"Net benefit",{"$f":"C12-C11","v":-5000000},{"$f":"D12-D11","v":2250000},{"$f":"E12-E11","v":2250000},{"$f":"F12-F11","v":2250000},{"$f":"G12-G11","v":2250000}]
[]
[null,"Results"]
[null,"Net Present Value",{"$f":"NPV(D7, C13:G13)","v":2542766.9987239079}]

{"sheet":"Workspace","index":2,"n_rows":16,"n_cols":10,"rows_kept":16,"cut":false,"hidden":false,"merged":[[1,8,1,12]]}
[]
[null,null,null,null,null,null,null,null,"Skills checklist"]
[]
[null,null,null,null,null,null,null,null,null,"Principles"]
[null,null,null,null,null,null,null,null,null,"Deterministic cash flow & NPV"]
[null,null,null,null,null,null,null,null,null,"Analytic solutions"]
[null,null,null,null,null,null,null,null,null,"RAND() function"]
[null,null,null,null,null,null,null,null,null,"HDR PRNG"]
[null,null,null,null,null,null,null,null,null,"Uniform distribution"]
[null,null,null,null,null,null,null,null,null,"Three-variable model"]
[null,null,null,null,null,null,null,null,null,"Excel's What-If Data Tables"]
[null,null,null,null,null,null,null,null,null,"COUNTIF() and AVERAGE() functions"]
[null,null,null,null,null,null,null,null,null,"Dynamic histograms"]
[null,null,null,null,null,null,null,null,null,"Triangular and binary distributions"]
[null,null,null,null,null,null,null,null,null,"Build a model from scratch"]
[null,null,null,null,null,null,null,null,null,"Optional material"]

{"sheet":"HDR PRNG","index":3,"n_rows":20,"n_cols":9,"rows_kept":20,"cut":false,"hidden":false,"merged":[[14,2,15,9],[17,7,22,9],[1,8,4,15],[1,7,4,7],[11,1,12,10],[6,4,6,15],[7,4,7,15],[8,4,8,15]]}
["Hubbard Decision Research PRNG"]
["Trial ID",7,null,null,null,null,null,"Formula Text","rand = ((mod((mod(mod(999999999999989,mod(trialID*2499997+varID*1800451,7450589)*4658+7450581)*383,99991)*7440893+mod(mod(999999999999989,mod(trialID*2246527+varID*2399993,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32"]
[]
[null,"Variable ID","HDR PRNG"]
[null,1000,{"$f":"((MOD((MOD(MOD(999999999999989,MOD($B$2*2499997+B5*1800451,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD($B$2*2246527+B5*2399993,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":0.93461240420583636},"← Copy this cell to use the PRNG in your exercises"]
[]
[null,"Dimension","1st Term","2nd Term","Description"]
[null,"Trial",2499997,2246527,"This represents a unique identifier for a given scenario in a simulation. This 8 decimal digit identifier allows for up to 100 million unique trials for each variable in a model."]
[null,"Variable",1800451,2399993,"This is a unique identifier for a variable. It would be an 8-digit variable ID allowing for up to 100 million unique variables. For example, if “Monthly Demand for Product X” and “average time spent in activity Y” were variables in a model, they would each be given unique variable IDs. Organizations may structure their Variables IDs so that related variables are in groups. For example, perhaps all marketing and sales related variables have “11” for the first two digits and all cybersecurity related variables have “73” for the first two digits, and so on. Variable IDs could be assigned on an ad hoc basis but a large organization making many models with a lot of shared variables would want to develop an internal library of assigned variable IDs similar to an accountant’s “chart of accounts.” "]
[]
[]
[null,"Sampling Error Around Dieharder Tests Results"]
[null,null,null,null,null,null,null,"Figure 1: Sampling error around Dieharder tests results. This uses a Beta Distribution to with a prior of alpha=1 and beta=1 to compute a 90% confidence interval for estimate of mean weak/fails out Dieharder test suite. The top row of brackets are estimates of WEAK result rates and the bottom row are estimates of FAIL rates."]
[]
[null,"•","This uses a Beta Distribution with a prior of alpha=1 and beta=1 to compute a 90% confidence interval for the estimate of mean weak/fail rates in the Dieharder test suite. "]
[]
[]
[null,null,null,null,null,null,null,"The top row of brackets are estimates of WEAK result rates and the bottom row are estimates of FAIL rates."]
[null,null,null,null,null,null,"•"]
[null,null," "]

{"sheet":"Probabalistic Cash Flow HDR","index":4,"n_rows":17,"n_cols":20,"rows_kept":17,"cut":false,"hidden":false,"merged":[[0,10,0,11],[0,13,0,15],[16,1,17,1],[16,2,17,2],[1,10,2,11],[1,13,2,15],[2,2,2,5],[1,2,1,3]]}
["Probabalistic Cash Flow Example",null,null,null,null,null,null,null,null,null,"Data Table",null,null,"Histogram"]
["Trial ID: ",9,"Insert scroll bar.",null,null,null,null,null,null,null,"Build a data table with 500 scenarios.",null,null,"Enter the logic for a histogram below."]
[null,null,"Enter the formula for an inverse uniform in the Random Sample column."]
[null,"Input Variables",null,"Simulated Value","Min.","Max.","Variable ID","HDR PRNG",null,null,"Trial #","NPV",null,"Bin","Cumulative","Frequency"]
[null,"Percent reduction in labor cost",null,null,0.01,0.06]
[null,"Current total labor cost",null,null,50000000,90000000]
[null,"Initial development costs (2020)",null,null,3000000,8000000,null,null,null,null,null,null,null,null,null,null,null,null,null,"Insert histogram here."]
[null,"Cost of money",null,null,0.05,0.08]
[]
[null,"Cash Flow"]
[null,null,2020,2021,2022,2023,2024]
[null,"Total costs",{"$f":"D7","v":0}]
[null,"Total benefits",null,{"$f":"$D6*$D5","v":0},{"$f":"$D6*$D5","v":0},{"$f":"$D6*$D5","v":0},{"$f":"$D6*$D5","v":0}]
[null,"Net benefit",{"$f":"C13-C12","v":0},{"$f":"D13-D12","v":0},{"$f":"E13-E12","v":0},{"$f":"F13-F12","v":0},{"$f":"G13-G12","v":0}]
[]
[null,"Results",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Average NPV"]
[null,"Net Present Value",{"$f":"NPV(E8, C14:G14)","v":0},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"P(NPV<0)"]

{"sheet":"Distributions","index":5,"n_rows":17,"n_cols":6,"rows_kept":17,"cut":false,"hidden":false,"merged":[[4,0,4,7],[9,0,9,7],[14,0,14,7],[12,0,12,15]]}
["Selected Distributions"]
["Trial ID",7692]
[]
["Uniform"]
["One of the simplest  distributions you can use is the uniform distribution. There is no chance of a value being above the maximum or below the minimum, and every value between the min and max are equally likely.\n\n■■ When to use: When you know the minimum and maximum values, but any value in between is equally likely.\n■■ Examples: The proportion of people that would buy a product, number of employees that do some activity.\n■■ Mean = (min + max)/2\n■■ Simulated value = rand * (max - min) + min"]
["Simulated Value","Minimum","Mode or Probability","Maximum","Variable ID","HDR PRNG"]
[{"$f":"F7*(D7-B7)+B7","v":5.9139327961020172E-2},0,"N/A",1,1,{"$f":"(MOD((MOD(MOD(999999999999989,MOD($B$2*9929+E7*9721,31907)*4177+7450581)*30119,31607)*31607+MOD(MOD(997969999999967,MOD($B$2*9857+E7*9949,33493)*4051+7450581)*29633,31607))*1000981,4294967296)+0.5)/4294967296","v":5.9139327961020172E-2}]
[]
["Triangular"]
["For a triangular distribution, the UB and LB represent absolute limits. There is no chance that a value could be generated outside of these bounds. In addition to the UB and LB, this distribution also has a mode that can vary to any value between the UB and LB. This is sometimes useful as a substitute for a lognormal, when you want to set absolute limits on what the values can be but you want to skew the output in a way similar to the lognormal. It is useful in any situation where you know of absolute limits but the most likely value might not be in the middle, like the normal distribution.\n \n■■When to Use: When you want control over where the most likely value is compared to the range, and when the range has absolute limits.\n■■ Examples: Number of records lost if you think the most likely number is near the top of the range and yet you have a finite number of records you know cannot be exceeded.\n■■ Mean: =(min+mode+max)/3\n■■ Simulated value = IF(rand<(mode-min)/(max-min), 1, 0) * (min + SQRT(rand*(max-min)*(mode-min))) + IF(rand>= (mode-min)/(max-min), 1, 0) * (max - SQRT((1-rand) * (max - min) * (max - mode)))"]
["Random Result","Minimum","Mode or Probability","Maximum","Variable ID","HDR PRNG"]
[{"$f":"IF(F12<(C12-B12)/(D12-B12), 1, 0) * (B12 + SQRT(F12*(D12-B12)*(C12-B12))) + IF(F12>= (C12-B12)/(D12-B12), 1, 0) * (D12 - SQRT((1-F12) * (D12 - B12) * (D12 - C12)))","v":3.5071671801631101},1,3,4,2,{"$f":"(MOD((MOD(MOD(999999999999989,MOD($B$2*9929+E12*9721,31907)*4177+7450581)*30119,31607)*31607+MOD(MOD(997969999999967,MOD($B$2*9857+E12*9949,33493)*4051+7450581)*29633,31607))*1000981,4294967296)+0.5)/4294967296","v":0.91903860389720649}]
[]
["Binary"]
["Unlike the other distributions mentioned here, a discrete binary distribution (also known as a Bernoulli distribution) generates just two possible outcomes: success or failure. The probability of success is p and the probability of failure is q = (1 – p). For example, if success means to flip a fair coin heads‐up, the probability of success is p = .5, and the probability of failure is q = (1 – .5) = .5.\n\n■■ When to use: This is used in either/or situations—something either happens or it doesn’t.\n■■ Example: The occurrence of a data breach in a given period of time.\n■■ Mean: =P\n■■ Simulated value = if(rand<probability, 1, 0)"]
["Random Result","Minimum","Mode or Probability","Maximum","Variable ID","HDR PRNG"]
[{"$f":"IF(F17<C17,1,0)","v":0},"N/A",0.3,"N/A",3,{"$f":"(MOD((MOD(MOD(999999999999989,MOD($B$2*9929+E17*9721,31907)*4177+7450581)*30119,31607)*31607+MOD(MOD(997969999999967,MOD($B$2*9857+E17*9949,33493)*4051+7450581)*29633,31607))*1000981,4294967296)+0.5)/4294967296","v":0.98801799432840198}]

{"sheet":"UBDM Example","index":6,"n_rows":504,"n_cols":22,"rows_kept":504,"cut":false,"hidden":false,"merged":[[0,11,0,12],[0,14,0,16],[26,1,27,1],[26,2,27,2]]}
["UBDM Example",null,null,null,null,null,null,null,null,null,null,"Data Table",null,null,"Histogram"]
[null,null,"Trial ID: ",20]
[null,"Input Variables","Simulated value","Lower Bound or Minimum","Mode or Prob","Upper Bound or Max","Shape","Variable ID","HDR PRNG",null,null,"Trial #","NPV",null,"Bin","Cumulative","Frequency"]
[null,"Time Spent in Document Mgt",{"$f":"I4*(F4-D4)+D4","v":0.29872247318853623},0.05,null,0.3,"Uniform",1,{"$f":"((MOD((MOD(MOD(999999999999989,MOD(D$2*2499997+H4*1800451,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD(D$2*2246527+H4*2399993,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":0.99488989275414497},null,null,null,{"$f":"C27","v":3931105.9247893621},null,-15000000,{"$f":"COUNTIF(M$5:M$504, \"<\"&O4)","v":0},{"$f":"COUNTIF(M$5:M$504, \"<=\"&O4)/COUNT($L$5:$L$504)","v":0}]
[null,"Reduction in time spent in Doc Mgt",{"$f":"IF(I5<(E5-D5)/(F5-D5), 1, 0) * (D5 + SQRT(I5*(F5-D5)*(E5-D5))) + IF(I5>= (E5-D5)/(F5-D5), 1, 0) * (F5 - SQRT((1-I5) * (F5 - D5) * (F5 - E5)))","v":0.14287882684396241},0.05,0.2,0.3,"Triangular",2,0.23003937269095331,null,null,1,-4414419.1854197457,null,{"$f":"O4+1000000","v":-14000000},{"$f":"COUNTIF(M$5:M$504, \"<\"&O5)","v":0},{"$f":"COUNTIF(M$5:M$504, \"<=\"&O5)/COUNT($L$5:$L$504)-SUM(Q$4:Q4)","v":0}]
[null,"Loaded cost of labor (per FTE)",{"$f":"_xlfn.LOGNORM.INV(I6,(LN(F6)+LN(D6))/2,(LN(F6)-LN(D6))/3.29)","v":81986.073058420632},70000,null,90000,"Lognormal",3,0.66425859194714576,null,null,2,-5361932.1421967642,null,{"$f":"O5+1000000","v":-13000000},0,{"$f":"COUNTIF(M$5:M$504, \"<=\"&O6)/COUNT($L$5:$L$504)-SUM(Q$4:Q5)","v":0}]
[null,"Staff involved in tasks",{"$f":"IF(I7<(E7-D7)/(F7-D7), 1, 0) * (D7 + SQRT(I7*(F7-D7)*(E7-D7))) + IF(I7>= (E7-D7)/(F7-D7), 1, 0) * (F7 - SQRT((1-I7) * (F7 - D7) * (F7 - E7)))","v":1197.4812386120186},1000,1200,1400,"Triangular",4,0.48748549504671246,null,null,3,-598716.74388951017,null,-12000000,0,{"$f":"COUNTIF(M$5:M$504, \"<=\"&O7)/COUNT($L$5:$L$504)-SUM(Q$4:Q6)","v":0}]
[null,"Growth in volumes",{"$f":"_xlfn.NORM.INV(I8,(F8+D8)/2,(F8-D8)/3.29)","v":8.2873729036415655E-3},0,null,0.08,"Normal",5,9.6085803699679673E-2,null,null,4,5805005.8139946479,null,-11000000,0,{"$f":"COUNTIF(M$5:M$504, \"<=\"&O8)/COUNT($L$5:$L$504)-SUM(Q$4:Q7)","v":0}]
[null,"Initial development costs",{"$f":"IF(I9<(E9-D9)/(F9-D9), 1, 0) * (D9 + SQRT(I9*(F9-D9)*(E9-D9))) + IF(I9>= (E9-D9)/(F9-D9), 1, 0) * (F9 - SQRT((1-I9) * (F9 - D9) * (F9 - E9)))","v":7559633.7429370284},5000000,7000000,9000000,"Triangular",6,0.7406681306893006,null,null,5,4652849.2571066748,null,-10000000,2,{"$f":"COUNTIF(M$5:M$504, \"<=\"&O9)/COUNT($L$5:$L$504)-SUM(Q$4:Q8)","v":4.0000000000000001E-3}]
[null,"Ongoing Maintenance Costs",{"$f":"_xlfn.LOGNORM.INV(I10,(LN(F10)+LN(D10))/2,(LN(F10)-LN(D10))/3.29)","v":732475.24686795066},500000,null,1000000,"Lognormal",7,0.56643409479875118,null,null,6,-3265654.9407357355,null,-9000000,5,{"$f":"COUNTIF(M$5:M$504, \"<=\"&O10)/COUNT($L$5:$L$504)-SUM(Q$4:Q9)","v":6.0000000000000001E-3}]
[null,"Chance of cancellation",{"$f":"IF(I11<E11, 1, 0)","v":0},null,0.04,null,"Binary",8,0.87981117202434689,null,null,7,-2709723.5920459908,null,-8000000,11,{"$f":"COUNTIF(M$5:M$504, \"<=\"&O11)/COUNT($L$5:$L$504)-SUM(Q$4:Q10)","v":1.1999999999999999E-2}]
[null,"Cost of money",{"$f":"_xlfn.LOGNORM.INV(I12,(LN(F12)+LN(D12))/2,(LN(F12)-LN(D12))/3.29)","v":7.7564625581432456E-2},0.03,null,0.09,"Lognormal",9,0.88487117306794971,null,null,8,5397706.2159482082,null,-7000000,20,{"$f":"COUNTIF(M$5:M$504, \"<=\"&O12)/COUNT($L$5:$L$504)-SUM(Q$4:Q11)","v":1.8000000000000002E-2}]
[null,null,null,null,null,null,null,null,null,null,null,9,8232363.1995269014,null,-6000000,36,{"$f":"COUNTIF(M$5:M$504, \"<=\"&O13)/COUNT($L$5:$L$504)-SUM(Q$4:Q12)","v":3.1999999999999994E-2}]
[null,"Cash Flow",null,null,null,null,null,null,null,null,null,10,-3601010.3007983593,null,-5000000,51,{"$f":"COUNTIF(M$5:M$504, \"<=\"&O14)/COUNT($L$5:$L$504)-SUM(Q$4:Q13)","v":0.03}]
[null,null,2020,2021,2022,2023,2024,null,null,null,null,11,7650683.5402133232,null,-4000000,81,{"$f":"COUNTIF(M$5:M$504, \"<=\"&O15)/COUNT($L$5:$L$504)-SUM(Q$4:Q14)","v":6.0000000000000012E-2},null,null,null,"Average NPV",{"$f":"AVERAGE(M5:M504)","v":1863460.2349188402}]
[null,"Costs",null,null,null,null,null,null,null,null,null,12,1940230.4310806238,null,-3000000,126,{"$f":"COUNTIF(M$5:M$504, \"<=\"&O16)/COUNT($L$5:$L$504)-SUM(Q$4:Q15)","v":0.09},null,null,null,"P(NPV<0)",{"$f":"COUNTIF(M5:M504, \"<0\")/500","v":0.44}]
[null,"Initial dev costs",{"$f":"C9","v":7559633.7429370284},null,null,null,null,null,null,null,null,13,-3286409.0040524052,null,-2000000,158,{"$f":"COUNTIF(M$5:M$504, \"<=\"&O17)/COUNT($L$5:$L$504)-SUM(Q$4:Q16)","v":6.4000000000000001E-2}]
[null,"Ongoing maint.",null,{"$f":"$C10","v":732475.24686795066},{"$f":"$C10","v":732475.24686795066},732475.24686795066,732475.24686795066,null,null,null,null,14,-2040321.3222719454,null,-1000000,189,{"$f":"COUNTIF(M$5:M$504, \"<=\"&O18)/COUNT($L$5:$L$504)-SUM(Q$4:Q17)","v":6.2E-2}]
[null,"Cancelled?",{"$f":"C11","v":0},null,null,null,null,null,null,null,null,15,-2870102.5303224768,null,0,220,{"$f":"COUNTIF(M$5:M$504, \"<=\"&O19)/COUNT($L$5:$L$504)-SUM(Q$4:Q18)","v":6.2E-2}]
[null,"Benefits",null,null,null,null,null,null,null,null,null,16,11632467.652074251,null,1000000,246,{"$f":"COUNTIF(M$5:M$504, \"<=\"&O20)/COUNT($L$5:$L$504)-SUM(Q$4:Q19)","v":5.1999999999999991E-2}]
[null,"Staf w/growth",null,{"$f":"$C7*(1+$C8)^(D15-$C15)","v":1207.4052121815109},{"$f":"$C7*(1+$C8)^(E15-$C15)","v":1217.4114294206593},1227.5005719134235,1237.6733268923033,null,null,null,null,17,12034183.907006055,null,2000000,276,{"$f":"COUNTIF(M$5:M$504, \"<=\"&O21)/COUNT($L$5:$L$504)-SUM(Q$4:Q20)","v":6.0000000000000053E-2}]
[null,"Cost of labor in doc mgt",null,{"$f":"D21*$C6*$C4","v":29570660.675781965},{"$f":"E21*$C6*$C4","v":29815723.767809212},30062817.789065015,30311959.570617225,null,null,null,null,18,2573829.7010300653,null,3000000,307,{"$f":"COUNTIF(M$5:M$504, \"<=\"&O22)/COUNT($L$5:$L$504)-SUM(Q$4:Q21)","v":6.1999999999999944E-2}]
[null,"Labor savings",null,{"$f":"D22*$C5*(1-$C19)","v":4225021.30635662},{"$f":"E22*$C5*(1-$C19)","v":4260035.6334482273},4295340.1373254135,4330937.2227914082,null,null,null,null,19,875608.02355639031,null,4000000,335,{"$f":"COUNTIF(M$5:M$504, \"<=\"&O23)/COUNT($L$5:$L$504)-SUM(Q$4:Q22)","v":5.600000000000005E-2}]
[null,"Net benefit",{"$f":"C23-C18-C17","v":-7559633.7429370284},{"$f":"D23-D18-D17","v":3492546.0594886695},{"$f":"E23-E18-E17","v":3527560.3865802768},3562864.890457463,{"$f":"G23-G18-G17","v":3598461.9759234576},null,null,null,null,20,3931105.9247893621,null,5000000,355,{"$f":"COUNTIF(M$5:M$504, \"<=\"&O24)/COUNT($L$5:$L$504)-SUM(Q$4:Q23)","v":3.9999999999999925E-2}]
[null,null,null,null,null,null,null,null,null,null,null,21,4239990.0655378904,null,6000000,377,{"$f":"COUNTIF(M$5:M$504, \"<=\"&O25)/COUNT($L$5:$L$504)-SUM(Q$4:Q24)","v":4.4000000000000039E-2}]
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[null,"Net Present Value",{"$f":"NPV(C12, C24:G24)","v":3931105.9247893621},null,null,null,null,null,null,null,null,23,-5842282.502242432,null,8000000,416,{"$f":"COUNTIF(M$5:M$504, \"<=\"&O27)/COUNT($L$5:$L$504)-SUM(Q$4:Q26)","v":4.1999999999999926E-2}]
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{"sheet":"Final Slides","index":7,"n_rows":50,"n_cols":4,"rows_kept":50,"cut":false,"hidden":false,"merged":[[1,1,2,10],[6,2,7,9],[10,6,13,9],[21,1,22,10],[41,1,42,10]]}
[]
[null,"Performance Considerations"]
[]
[]
[null,"•","Balance number of scenarios and sampling error."]
[]
[null,"•","Use a fixed set of random numbers applied to each agent (primarily for agent-based prioritization)."]
[]
[]
[null,"•","Limit the number of cross sheet references."]
[]
[null,"•","Avoid using volatile functions."]
[null,null,null,"RAND()"]
[null,null,null,"NOW()"]
[null,null,null,"TODAY()"]
[null,null,null,"OFFSET()"]
[null,null,null,"CELL()"]
[null,null,null,"INDIRECT()"]
[null,null,null,"INFO()"]
[]
[]
[null,"Aspirational Goals"]
[]
[]
[null,"•","Agent-based Models"]
[]
[null,"•","Markov chain Models"]
[]
[null,"•","Risk Tolerance & Expected Utility"]
[]
[null,"•","Information Value"]
[]
[null,"•","Excel's New Dynamic Array Functions"]
[null,null,null,"FILTER() – allows you to filter a range of data based on criteria you define."]
[null,null,null,"RANDARRAY() – returns an array of random numbers between 0 and 1."]
[null,null,null,"SEQUENCE() – allows you to generate a list of sequential numbers in an array, such as 1, 2, 3, 4."]
[null,null,null,"SORT() – sorts the contents of a range or array."]
[null,null,null,"UNIQUE() – returns a list of unique values in a list or range."]
[]
[]
[]
[null,"Contact"]
[]
[]
[]
[null,null,"Doug Hubbard"]
[null,null,"Hubbard Decision Research"]
[null,null,"dwhubbard@hubbardresearch.com"]
[null,null,"www.hubbardresearch.com"]
[null,null,"630 858 2788"]