Toy problem: A dataset that has two variables- extra Time spent by a high schooler studying (percent of his recreational time). This variable, we assume, affects the School he finally gets into.n = 10000Time = round(runif(n)*100,1)School = sample(LETTERS[1:3],n,replace = TRUE)data = data.frame(Time, School)I am trying to estimate the probability of admission to each school, given Time put in as a continuous variable.One simplification of the problem is to convert Time variable to categorical and then estimate empirical probabilities for the system as below.data$Time_Category = 1data[data$Time>=25,]$Time_Category <- 2data[data$Time>=50,]$Time_Category <- 3data[data$Time>=75,]$Time_Category <- 4test = table(data$Time_Category,data$School)trans_matrix = prop.table(test,1)I am falling short of identifying which method will solve this problem for a continuous variable Time. Any direction will be useful.
Estimating probability of observed states
r;probability