Quizmaster

Learning objectives

What you will be able to explain

Section 01

The scalar formulas specialize the matrix Gaussian identities.

Guided checkpoint

Let $x\sim N(mu,sigma^2)$ .

Source: Appendix A.1, p. 64

E[x^2]=Var(x)+E[x]^2=4+9=13

Guided checkpoint

If $E[x]=3$ and $Var(x)=4$ , compute $E[x^2]$ .

Source: Appendix A.1, p. 64

Gaussian multiplication is most transparent in natural/precision parameters.

Guided checkpoint

For scalar Gaussian factors.

Source: Appendix A.1, p. 64

Section 02

Independent Gaussian convolution adds means and variances.

Guided checkpoint

If $x\sim N(mu_x,sigma_x^2)$ and $y\sim N(mu_y,sigma_y^2)$ independently, what is $x+y$ ?

Source: Appendix A.1, p. 64

Total variance separates within-component and between-component contributions.

Guided checkpoint

For $p(x)=sum_k pi_k N(x|mu_k,sigma_k^2)$ .

Source: Appendix A.2, p. 65

Mean is zero; within variance is 1 and between-mean variance is 1, totaling 2.

Guided checkpoint

Equal weights combine $N(-1,1)$ and $N(1,1)$ . Compute mixture variance.

Source: Appendix A.2, p. 65

Knowledge check

The quiz now follows the same concepts in scored form. You can return to this lesson from the quiz whenever a gap appears.