diff --git a/source/sec-Continuous-RVs.ptx b/source/sec-Continuous-RVs.ptx
index 161c649..b19ea2b 100644
--- a/source/sec-Continuous-RVs.ptx
+++ b/source/sec-Continuous-RVs.ptx
@@ -298,13 +298,42 @@
-
+
A continuous random variable X taking values in [1, 4] has p.d.f.
f(x) = k(x - \sqrt{x}) for some constant k.
- What is the value of k?
-
+
+
+
+
+
+
+ What is the value of k?
+
+
+
+
+
+ k = \frac{6}{17}.
+
+
+
+
+
+
+
+
+ Find \Pr(2 \leq X \leq 3).
+
+
+
+
+
+ \Pr(2 \leq X \leq 3) \approx 0.325
+
+
+
@@ -318,6 +347,12 @@
to find \Pr\left(1 \leq X \leq \frac{3}{2}\right).
+
+
+
+ \frac{1}{2}\left(\frac{x^2}{2} - \frac{1}{x}\right) + \frac{1}{4}. \Pr\left(1 \leq X \leq \frac{3}{2}\right) \approx 0.479.
+
+
@@ -329,8 +364,29 @@
f(x).
+
+
+
+ f(x) = x^2 - 2x.
+
+
+
+
+
+ Let T \sim \Exp(3).
+ Find \Pr(1 \leq T \leq 3) and \Pr(T \geq 0.5).
+
+
+
+
+
+ \Pr(1 \leq T \leq 3) \approx 0.050. \Pr(T \geq 0.5) \approx 0.223.
+
+
+
+
\ No newline at end of file
diff --git a/source/sec-Discrete-RVs.ptx b/source/sec-Discrete-RVs.ptx
index 64fbaba..51c7689 100644
--- a/source/sec-Discrete-RVs.ptx
+++ b/source/sec-Discrete-RVs.ptx
@@ -398,6 +398,13 @@
Which flip has the highest chance of being the first flip to come up heads?
+
+
+
+ \Pr(T = k) = 0.6^{k-1} \cdot 0.4, so every additional flip multiplies the probability by 0.6.
+ Therefore, the highest value for \Pr(T = k) occurs when k = 1, in which case \Pr(T = 1) = 0.4.
+
+