{"id":189,"date":"2023-05-05T15:53:39","date_gmt":"2023-05-05T19:53:39","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/businessanalytics\/chapter\/__unknown__\/"},"modified":"2023-05-08T14:10:33","modified_gmt":"2023-05-08T18:10:33","slug":"intro_simulations","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/businessanalytics\/chapter\/intro_simulations\/","title":{"raw":"Introduction to Simulations","rendered":"Introduction to Simulations"},"content":{"raw":"
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The Monte Carlo method<\/em><\/h1>\r\n

What is a simulation?<\/h2>\r\n

Let\u2019s roll a lot of dice. Every time we roll, that\u2019s a simulation. This allows us to find experimental probabilities:<\/p>\r\n

<\/p>\r\n\r\n<\/div>\r\n

[latex]P(\\textrm{rolling a }6) = \\frac{ \\textrm{Number of sixes}}{\\textrm{Number of total rolls}}[\/latex]<\/p>\r\n \r\n

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Law of Large Numbers (or law of averages)<\/h2>\r\n

As the total number of simulations gets larger, the experimental probability gets closer to the theoretical probability:<\/p>\r\n

\\[P(\\textrm{rolling a 6})\\rightarrow \\frac{1}{6}\\]<\/span><\/p>\r\n\r\n

Can computers find random numbers?<\/h2>\r\n

Not exactly! But what they can do is generate large amounts of pseudorandom<\/em> numbers. That is, a computer will use complex algorithms to find something that is close enough to random to satisfy most mathematicians.<\/p>\r\n

EXCEL:<\/p>\r\n

Our major tools will be the Excel functions: RAND()<\/code> and RANDBETWEEN(a,b)<\/code>. To simulate a large lumber of dice rolls, we use the function RANDBETWEEN(1,6)<\/code>, which randomly chooses a number between 1 and 6.<\/p>\r\n

R:<\/p>\r\n

R is easier: we will use \u201cr\u201d commands (rnorm()<\/code>, rpois()<\/code>, rbinom()<\/code>, ect) to generate strings of random numbers.<\/p>\r\n\r\n

Examples of simulations in Business<\/h2>\r\n

Simulations can do more than let us roll pretend dice. They can be used to model various real-world situations such as:<\/p>\r\n\r\n