Completed exercise 1.

Added `zbuild` manifest to build the diagrams and images.

code/1.R

@@ -0,0 +1,59 @@
+library(ggplot2)
+library(gridExtra)
+
+simulate <- function(alpha, beta, output_file) {
+  # 2-DTMC transition matrix
+  p <- matrix(
+    c(
+      c(alpha, 1 - alpha),
+      c(beta, 1 - beta)
+    ),
+    nrow = 2,
+    ncol = 2,
+    byrow = TRUE
+  )
+
+  # DTMC mean
+  p_avg <- p[1, 2] / (1 + p[2, 1] - p[1, 1])
+
+  points_len <- 200
+
+  # 2-DTMC simulation
+  points1 <- c()
+  current_state <- 0
+  for (i in 1:points_len) {
+    # Extracts probability of transition to same state
+    prob <- p[current_state + 1, current_state + 1]
+
+    # Changes state if no success
+    if (rbinom(1, 1, prob) == 0) {
+      current_state <- (current_state + 1) %% 2
+    }
+
+    points1[length(points1) + 1] <- current_state
+  }
+
+  # Bernoulli process simulation
+  points2 <- lapply(1:points_len, function(...) rbinom(1, 1, p_avg))
+  points2 <- unlist(points2)
+
+  # Organize into data frames
+  data1 <- data.frame(x = seq_along(points1), y = points1)
+  data2 <- data.frame(x = seq_along(points2), y = points2)
+
+  p1 <- ggplot(data1) +
+    geom_point(aes(.data$x, .data$y)) +
+    scale_y_continuous("2-DTMC")
+  p2 <- ggplot(data2) +
+    geom_point(aes(.data$x, .data$y)) +
+    scale_y_continuous("Bernoulli")
+  p3 <- grid.arrange(p1, p2, ncol = 1)
+  ggsave(p3, file = output_file, device = "svg")
+}
+
+set.seed(0)
+pdf(NULL)
+simulate(0.1, 0.1, "images/1a (α=0.1, β=0.1).svg")
+simulate(0.5, 0.5, "images/1a (α=0.5, β=0.5).svg")
+simulate(0.9, 0.9, "images/1a (α=0.9, β=0.9).svg")
+simulate(0.9, 0.1, "images/1b (α=0.9, β=0.1).svg")