# ::Free Statistics and Forecasting Software::

v1.2.1

### :: Exercise 1.13 - Free Statistics Software (Calculator) ::

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This free online software (calculator) computes a solution for Exercise 1.13 p. 14 (Introduction to Probability, 2nd ed.)

 Send output to: Browser Blue - Charts White Browser Black/White CSV Number of simulated days 36573010951460182521902555292032853650 Expected number of births in Large Hospital 4550556065707580859095100105110 Expected number of births in Small Hospital 152025303540 Percentage of Male births per day(for which the probability is computed) 0.60.650.70.750.80.850.9 Chart options Width: Height:

 Source code of R module par1 <- as.numeric(par1) par2 <- as.numeric(par2) par3 <- as.numeric(par3) par4 <- as.numeric(par4) numsuccessbig <- 0 numsuccesssmall <- 0 bighospital <- array(NA,dim=c(par1,par2)) smallhospital <- array(NA,dim=c(par1,par3)) bigprob <- array(NA,dim=par1) smallprob <- array(NA,dim=par1) for (i in 1:par1) { bighospital[i,] <- sample(c("F","M"),par2,replace=TRUE) if (as.matrix(table(bighospital[i,]))[2] > par4*par2) numsuccessbig = numsuccessbig + 1 bigprob[i] <- numsuccessbig/i smallhospital[i,] <- sample(c("F","M"),par3,replace=TRUE) if (as.matrix(table(smallhospital[i,]))[2] > par4*par3) numsuccesssmall = numsuccesssmall + 1 smallprob[i] <- numsuccesssmall/i } tbig <- as.matrix(table(bighospital)) tsmall <- as.matrix(table(smallhospital)) tbig tsmall numsuccessbig/par1 bigprob[par1] numsuccesssmall/par1 smallprob[par1] numsuccessbig/par1*365 bigprob[par1]*365 numsuccesssmall/par1*365 smallprob[par1]*365 bitmap(file="test1.png") plot(bigprob,col=2,main="Probability in Large Hospital",xlab="#simulated days",ylab="probability") dev.off() bitmap(file="test2.png") plot(smallprob,col=2,main="Probability in Small Hospital",xlab="#simulated days",ylab="probability") dev.off() load(file="createtable") a<-table.start() a<-table.row.start(a) a<-table.element(a,"Exercise 1.13 p. 14 (Introduction to Probability, 2nd ed.)",2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Number of simulated days",header=TRUE) a<-table.element(a,par1) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Expected number of births in Large Hospital",header=TRUE) a<-table.element(a,par2) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Expected number of births in Small Hospital",header=TRUE) a<-table.element(a,par3) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Percentage of Male births per day
(for which the probability is computed)",header=TRUE) a<-table.element(a,par4) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"#Females births in Large Hospital",header=TRUE) a<-table.element(a,tbig[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"#Males births in Large Hospital",header=TRUE) a<-table.element(a,tbig[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"#Female births in Small Hospital",header=TRUE) a<-table.element(a,tsmall[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"#Male births in Small Hospital",header=TRUE) a<-table.element(a,tsmall[2]) a<-table.row.end(a) a<-table.row.start(a) dum1 <- paste("Probability of more than", par4*100, sep=" ") dum <- paste(dum1, "% of male births in Large Hospital", sep=" ") a<-table.element(a, dum, header=TRUE) a<-table.element(a, bigprob[par1]) a<-table.row.end(a) dum <- paste(dum1, "% of male births in Small Hospital", sep=" ") a<-table.element(a, dum, header=TRUE) a<-table.element(a, smallprob[par1]) a<-table.row.end(a) a<-table.row.start(a) dum1 <- paste("#Days per Year when more than", par4*100, sep=" ") dum <- paste(dum1, "% of male births occur in Large Hospital", sep=" ") a<-table.element(a, dum, header=TRUE) a<-table.element(a, bigprob[par1]*365) a<-table.row.end(a) dum <- paste(dum1, "% of male births occur in Small Hospital", sep=" ") a<-table.element(a, dum, header=TRUE) a<-table.element(a, smallprob[par1]*365) a<-table.row.end(a) a<-table.end(a) table.save(a,file="mytable.tab")
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 Cite this software as: Wessa P., (2019), Excercise 1.13 of Introduction to Probability (v1.0.4) in Free Statistics Software (v1.2.1), Office for Research Development and Education, URL http://www.wessa.net/rwasp_babies.wasp/ The R code is based on : Grinstead, Charles and Laurie Snell, Introduction to Probability, http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html
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