diff --git a/source/main.ptx b/source/main.ptx
index 3675fc0..05b796d 100644
--- a/source/main.ptx
+++ b/source/main.ptx
@@ -34,6 +34,7 @@
Quizzes
+
diff --git a/source/notes/1-29.ptx b/source/notes/1-29.ptx
index 3397a0e..d5cee30 100644
--- a/source/notes/1-29.ptx
+++ b/source/notes/1-29.ptx
@@ -307,7 +307,7 @@
Let N be the number of heads in n coin flips with bias p.
Then N\sim \Bin(n, p).
- \E)N) = \sum_{i=0}^n i\cdot b(i; n, p) = \sum_{i = 0}^n i \cdot {n \choose i} p^i (1-p)^{n - i}.
+ \E(N) = \sum_{i=0}^n i\cdot b(i; n, p) = \sum_{i = 0}^n i \cdot {n \choose i} p^i (1-p)^{n - i}.
Gross.
diff --git a/source/quizzes/quiz-02.ptx b/source/quizzes/quiz-02.ptx
new file mode 100644
index 0000000..2f0778e
--- /dev/null
+++ b/source/quizzes/quiz-02.ptx
@@ -0,0 +1,205 @@
+
+
+
+
+ Quiz 2
+
+
+
+
+ The following work should be completed individually.
+ Use of notes or textbooks is not allowed.
+ You may use a scientific calculator, not a graphing calculator or phone app.
+
+
+
+ Show all work unless instructed otherwise.
+
+
+
+
+
+
+
+
+
+ Write either True or False for each of the following statements.
+ No justification is required.
+
+
+
+
+
+
+
+ Let n, k be integers with 0 \leq k \leq n.
+ Then {n\choose k} = {n \choose n - k}.
+
+
+
+
+
+ True.
+
+
+
+
+
+
+
+
+ Suppose X is a continuous random variable with pdf f(x) and cdf F(x).
+ Then \displaystyle{\int_a^b f(x)\ dx = F(b) - F(a)}.
+
+
+
+
+
+ True.
+
+
+
+
+
+
+
+
+ Suppose X is a random variable taking values between 0 and 6.
+ Then \E(X) = 3.
+
+
+
+
+
+ False.
+
+
+
+
+
+
+
+
+ Consider the joint distribution for X and Y below.
+
+
+
+ Joint Distribution
+
+
+
+ |
+ X = 0 |
+ X = 1 |
+ X = 2 |
+
+
+
+ | Y = 0 |
+ 0.1 |
+ 0.05 |
+ 0.1 |
+
+
+
+ | Y = 1 |
+ 0.3 |
+ 0.15 |
+ 0.3 |
+
+
+
+
+
+
+
+
+
+ Find the marginal distributions for X and Y.
+
+
+
+
+
+
+ \Pr(X = 0) \amp = 0.1 + 0.3 = 0.4
+ \Pr(X = 1) \amp = 0.05 + 0.15 = 0.2
+ \Pr(X = 2) \amp = 0.1 + 0.3 = 0.4
+ \Pr(Y = 0) \amp = 0.1 + 0.05 + 0.1 = 0.25
+ \Pr(Y = 1) \amp = 0.3 + 0.15 + 0.3 = 0.75
+
+
+
+
+
+
+
+
+
+ Are X and Y independent?
+
+
+
+
+
+
+ \Pr(X = 2, Y = 0) \amp = 0.2
+ \Pr(X = 2)\Pr(Y = 0) \amp = (0.4)(0.25) = 0.1
+
+ Since 0.2 \neq 0.1, X and Y are not independent.
+
+
+
+
+
+
+
+
+
+
+
+ Suppose a continuous random variable X taking values in [0, 1] has cdf F(x) = 2x^2 - x^4.
+
+
+
+
+
+
+
+ Find the pdf f(x).
+
+
+
+
+
+
+ f(x) = F'(x) = 4x - 4x^3.
+
+
+
+
+
+
+
+
+
+ Find \E(X).
+
+
+
+
+
+
+ \E(X) \amp = \int_0^1 x f(x)\ dx
+ \amp = \int_0^1 x (4x - 4x^3)\ dx
+ \amp = \int_0^1 4x^2 - 4x^4\ dx
+ \amp = \frac{4x^2}{3} - \frac{4x^5}{5}\bigg|_0^1
+ \amp = \left(\frac{4}{3} - \frac{4}{5}\right) - (0)
+ \amp = \frac{8}{15} \approx 0.533.
+
+
+
+
+
+
+
\ No newline at end of file