Homework 1

Due Friday September 8th at 5:00pm

Exercise 1

Let \(X_i \in \mathcal{X}\) for all \(i \in \{1, 2, \ldots\}\) and suppose our belief model for \(\mathbf{X} = \{ X_1, \ldots X_n \}\) is exchangeable for all \(n\). Show, using de Finetti’s theorem, that for all \(i \neq j\),

\[ Cov(X_i, X_j) \geq 0 \text{ and } \]

\[ Corr(X_i, X_j) \geq 0. \]

Exercise 2

• 2.2 from Hoff

Exercise 3

• 2.3 from Hoff

Exercise 4

• 2.6 from Hoff