Started work on problem 4.

4/script.R

@@ -0,0 +1,43 @@
+#!/bin/env Rscript
+
+# Set the seed for the RNG
+set.seed(4728)
+
+# Generate all the numbers
+nums_len <- 1550
+nums <- rexp(nums_len, rate = 21)
+
+# Then generate the cumulative sum of them
+# TODO: Is `max_time` even required?
+nums_cumsum <- cumsum(nums)
+max_time <- ceiling(nums_cumsum[nums_len])
+
+# Calculate a list of steps to discriminate
+# around unitary steps
+next_step <- 1
+steps <- sapply(nums_cumsum, function(x) {
+    if (x < next_step) {
+        FALSE
+    } else {
+        next_step <<- next_step + 1
+        TRUE
+    }
+})
+
+# Then count the occurrences within each unitary step
+cur_occurrences <- 0
+occurrences <- mapply(function(x, is_step) {
+    if (is_step) {
+        occurrences <- cur_occurrences
+        cur_occurrences <<- 1
+        occurrences
+    } else {
+        cur_occurrences <<- cur_occurrences + 1
+        NA
+    }
+}, nums_cumsum, steps)
+occurrences <- occurrences[!is.na(occurrences)]
+
+
+# TODO: Calculate expected value (theoretical) and
+#       compare it to the experimental value discovered here