The scientific method has four elements: Observe, Theorize, Predict, Test. For example, observations and careful thought...

 

 

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The scientific method has four elements: Observe, Theorize, Predict, Test. For example, observations and careful thought lead to the theory of dice sums presented in Sec- tion 1. In this project we will derive predictions from that theory and test them by means of a simulation. Follow the instructions, and present your results in a one-page technical report. (a) Using the theory presented at the end of Section 1, give a table of expected frequencies of all possible sums, in the experiment of tossing a pair of dice 10,000 times. Round all expected frequencies to the nearest integer. (b) Use R to carry out a simulation of 10000 tosses of two dice. Give the observed frequencies of all sums. Display these frequencies by adding an additional line to the table of expected frequencies from part (a). To do the simulation, activate R and do the following. 1. Set the random number seed to 26 * Y +K where Y denotes the last digit of the current year and K is the position in the alphabet of the first letter of your last name. If your last name begins with C, and the year is 2023, then your random number seed is 81, and so you would enter the command set.seed (81). 2. Create a variable, say ac, and set it equal to NULL by the command ac <- NULL. 3. Run a program like the one-line program for (i in 1:10000) {w <- sample (1:6,2,replace-TRUE); ac <- c(ac,sum (w))} The scientific method has four elements: Observe, Theorize, Predict, Test. For example, observations and careful thought lead to the theory of dice sums presented in Sec- tion 1. In this project we will derive predictions from that theory and test them by means of a simulation. Follow the instructions, and present your results in a one-page technical report. (a) Using the theory presented at the end of Section 1, give a table of expected frequencies of all possible sums, in the experiment of tossing a pair of dice 10,000 times. Round all expected frequencies to the nearest integer. (b) Use R to carry out a simulation of 10000 tosses of two dice. Give the observed frequencies of all sums. Display these frequencies by adding an additional line to the table of expected frequencies from part (a). To do the simulation, activate R and do the following. 1. Set the random number seed to 26 * Y +K where Y denotes the last digit of the current year and K is the position in the alphabet of the first letter of your last name. If your last name begins with C, and the year is 2023, then your random number seed is 81, and so you would enter the command set.seed (81). 2. Create a variable, say ac, and set it equal to NULL by the command ac <- NULL. 3. Run a program like the one-line program for (i in 1:10000) {w <- sample (1:6,2,replace-TRUE); ac <- c(ac,sum (w))}

Answer rating: 100% (QA)

R CODE rmlist ls PART a N 10000 E roundmatrixcseq212cseq16 seq51136N nro... View the full answer