Adding some answers

source/sec-Continuous-RVs.ptx

@@ -298,13 +298,42 @@
 
   <exercises xml:id="exercises-Continuous-RVs">
   <exercise>
-    <statement>
+    <introduction>
       <p>
         A continuous random variable <m>X</m> taking values in <m>[1, 4]</m> has p.d.f.
         <m>f(x) = k(x - \sqrt{x})</m> for some constant <m>k</m>.
-        What is the value of <m>k</m>?
       </p>
-    </statement>
+    </introduction>
+
+
+    <task>
+      <statement>
+        <p>
+          What is the value of <m>k</m>?
+        </p>
+      </statement>
+
+      <answer>
+        <p>
+          <m>k = \frac{6}{17}.</m>
+        </p>
+      </answer>
+    </task>
+
+
+    <task>
+      <statement>
+        <p>
+          Find <m>\Pr(2 \leq X \leq 3).</m>
+        </p>
+      </statement>
+
+      <answer>
+        <p>
+          <m>\Pr(2 \leq X \leq 3) \approx 0.325</m>
+        </p>
+      </answer>
+    </task>
   </exercise>
 
   <exercise>
@@ -318,6 +347,12 @@
         to find <m>\Pr\left(1 \leq X \leq \frac{3}{2}\right)</m>.
       </p>
     </statement>
+
+    <answer>
+      <p>
+        <m>\frac{1}{2}\left(\frac{x^2}{2} - \frac{1}{x}\right) + \frac{1}{4}</m>. <m>\Pr\left(1 \leq X \leq \frac{3}{2}\right) \approx 0.479.</m>
+      </p>
+    </answer>
   </exercise>
 
   <exercise>
@@ -329,8 +364,29 @@
         <m>f(x)</m>.
       </p>
     </statement>
+
+    <answer>
+      <p>
+        <m>f(x) = x^2 - 2x.</m>
+      </p>
+    </answer>
   </exercise>
 
+  <exercise>
+    <statement>
+      <p>
+        Let <m>T \sim \Exp(3)</m>.
+        Find <m>\Pr(1 \leq T \leq 3)</m> and <m>\Pr(T \geq 0.5)</m>.
+      </p>
+    </statement>
+
+    <answer>
+      <p>
+        <m>\Pr(1 \leq T \leq 3) \approx 0.050</m>. <m>\Pr(T \geq 0.5) \approx 0.223</m>.
+      </p>
+    </answer>
+  </exercise>
+  <!--
   <exercise>
     <statement>
       <p>
@@ -350,5 +406,5 @@
       </p>
     </statement>
   </exercise>
-  </exercises>
+  --> </exercises>
 </section>