Info3010, Final Exam Study Guide
Info3010, Final Exam Study Guide Info3010
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This 5 page Study Guide was uploaded by Rebecca Evans on Monday May 2, 2016. The Study Guide belongs to Info3010 at Tulane University taught by Srinivas Krishnamoorthy in Spring 2016. Since its upload, it has received 38 views. For similar materials see Business Modeling in Business at Tulane University.
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I was sick all last week and these notes were exactly what I needed to get caught up. Cheers!
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Date Created: 05/02/16
Final Exam Study Guide Example of Bayesian probability table: Agents says Positive Negative Successful (.8)(700) (.2)(700) 700 =560 =140 Actual Not Successful (300-255) (.85)(300) 300 =45 =255 605 395 1000 Conditional Probabilities P(Actually successful if agent says success)= 560/605 = 0.93 o Condition given: agent says success o Outcome: actually successful o Given condition, what is the probability of this outcome o Actually successful when agent say positive/total agent says positive P(actually unsuccessful if agent says negative)= 255/395= 0.65 Value of Information Sample information (from an imperfect test) Get values from rolled back decision tree o EV without info (ex. Don’t use agent) o EV with paid sample info (ex. Use agent) EVSI (Expected value of sample info)= EV with free sample info- EV without info Perfect Information EVPI (expected value of perfect information)= EV with free perfect info-EV without information Statistics concepts and excel Mean=average value of a set of observations o =AVERAGE(data values) Median=the middle value of a set of observations o =MEDIAN(data values) Standard deviation= measure the spread of data (how far data points are from mean) o Measured in the same units as data values o =STDEV(data values) Variance=(standard deviation) o =VAR(data points) Random variable=variable used to represent a random event o Discrete random variable=2 distinct outcomes/categories o Continuous random variable=can have decimal values/on a range (aka temp, weight) Histogram=use for discrete variable distribution o Y axis=frequency and x-axis=variable Continuous variable distribution=a curve (continuous line) o Y-axis=probability density and x-axis=variable o Uniform distribution=horizontal line; equal probability that will take on any value; each value in range is equally likely o Normal Distribution=highest probability in center and probability decreases as farther away from center; mean and median in the same place 68% of data within 1 standard deviation 95% data within 2 standard deviation 99.7% data within 3 standard deviation Normal Distribution Probabilities o Probability the x is greater/less than some value=total are to left or right of value o =NORM.DIST(value, mean, SD, 1) 1 is a binary code; 1=tell excel looking for area; 0=looking for height (**always use 1 in this course) o Can only find area to the left for area to the right= 1-total area to the left Because entire area under the curve is 1 (100% of probabilities) o Area between 2 values=area to left of larger value-area to the left of smaller value Ex. =NORM.DIST(25..)-NORM.DIST(15…) Inverse normal function o =NORM.INV(percentage, mean, SD) o Use when know the probability and trying to find value Z-score o (=Mean-value)/SD o Excel =STANDARDIZE(x, mean, SD) o Finding z-score is called normalization/standardization Monte Carol Simulation Use when decisions are made with random events Decision Tree: only random events with discrete outcomes o Discrete outcome=countable or limited number of outcomes Monte Carlo Simulation: random events w/ discrete and continuous outcomes o Continuous outcome=every possible outcome in a range o Can use parametric and structural sensitivity easily =RAND(x) function o Generates random number between 0 and 0.99999… o Re-calculates by pressing F9 (on PC) o Every number is equally likely (uniform distribution) o If make a histogram of 1000 trials of RAND fxn, all bars should be equal height Uniform distribution outside 0-1 o Ex. Get random number between 10 and 25: 10+(25-10) x RAND() 10= lower limit (25-10)=range Why? at least 10 (lower limit) and rand can be anywhere between 0-1 so multiply by range to put outcome between 10-25 o Get random integer values between 60 and 75 RANDBETWEEN(60,75) =RANDBETWEEN gives integer values only Simulating 2 outcome discrete distributions o Ex. Simulate event that may happen with probability of 0.4 =IF(RAND()<0.4, 1, 0) Why? Rand will give number between 0-1 0 0.4 1 Hit flop 40% 60% Binary 1=hit and 0=flop Random Number from a Normal Distribution Normal Distribution 3 2.5 2 1.5 1 0.5 0 0 0.2 0.4 0.6 0.8 1 1.2 NORM.INV(RAND, 100, 20)=will give number on x-axis normal distribution probability will create a norm distribution histogram use rand fxn to replace probability Develop a simulation model to determine the mean and standard deviation of daily revenue obtained from the sale of the super-duper doughnuts. Decision tree 0.4 32 o 0.3 33 0.3 34 Make range from 0-1 with 3 possible outcomes3 sub-ranges Boundary of ranges correspond with probabilities of each value 32 33 34 0 0.4 0.4 0.7 0.7 1 40% 30% 30% In excel B C D E 2 Demand 32 33 34 3 Probability 0.4 0.3 0.3 Simulation Calculations Demand: =IF(B10<C3,C2,IF(B10<C3+D3,D2,E2)) Revenue: selling price*min(demand, in stock) Or revenue=C6*IF(C10<C5,C10,C5) = selling price*if(demand<in stock, demand, in stock) Simulation Trials Link upper right box to revenue (next to trial #) Select entire tabledatawhat if analysisdata tableleave row input blankcolumn input=any random cell outside of the table (to trick excel) Use to simulate number of days in business and revenue Output Mean revenue=average(all trial cells) Standard deviation =stdev(all trial cells) Excel Cell*norm.inv(rand(), o Norm.inv function o Know percentage and find corresponding x value o Norm.inv(probability, mean, standard deviation) Simulate 1,00 trials o Link upper right corner of table to the revenue you want to simulate (the total revenue) o Link tells excel what the output we want simulated is o Select entire tabledatawhat-if analysisdata tableleave row input blank and choose random cell for column input Predictive Modeling Linear regression Analytical tool for: o Relationship b/w variable o Prediction about variable Regression in Excel =SLOPE(y values, x values) =INTERCEPT(y values, x values) Using data/data analysis/regression option 2 R R = variation in the predicted variable explained by our model/total variation in the predicted variable It measures “goodness of fit” o Tells us how well line fits data on the scatter chart Extreme scenarios: 2 o R =1: perfect fit, every point falls on line of best fit o R =0: no relations ship, the line of best fit is horizontal to x-axis and points are randomly scatter around it 2 o R values range from 0-1 or as a % from 0-100% o Good R is high, but often is not in business (but at least some of the variation is being explained) Excel norm.inv(rand(), o Norm.inv function o Know percentage and find corresponding x value o Norm.inv(probability, mean, standard deviation) Simulate 1,00 trials o Link upper right corner of table to the revenue you want to simulate (the total revenue) o Link tells excel what the output we want simulated is o Select entire tabledatawhat-if analysisdata tableleave row input blank and choose random cell for column input Point and interval prediction Point prediction: estimate 1 number 99% Interval prediction: o Point prediction+/- (3)(standard error) o 99% interval3 standard deviations o 95% interval2 standard deviations Standard error found under “regression statistics” table
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