# for topic 11 a discrete probabilities
    # create our table
    # first get the individual measures
vals  <-  c( 14, 17, 18, 22, 23, 25 )
    # then get the number of times each measure 
    # needs to happen
marble <- c( 23, 34, 19, 25, 12, 17 )
    # then make the population of marbles
all_marbles <- rep( vals, marble)
    # and look at them
all_marbles
# just to be sure we conform, make a 
# frequency table
source("../make_freq_table.R")
make_freq_table(all_marbles )
    # then we can find the mean and standard 
    # deviation of our population of marbles
mean( all_marbles )
    #  remember this is a population
source( "../pop_sd.R")
pop_sd( all_marbles )
    # But what if we had a different population 
    # that still conformed to the probabilities 
    # that we were given
big_pop <- rep( all_marbles, 7 )
    # just to be sure we conform, make a 
    # frequency table
make_freq_table( big_pop )
     # find the mean and standard deviation of this
mean( big_pop )
pop_sd( big_pop )