Overview Estimation

Year\Exam	Done $✓$	Permitted Aids	Notes
2018		D	Prob 1: a) Veldig syre. Hva skjer med $p(\mathbf{r})?$ Prob2: a) Use neyman pearson
2019
---Pierluigi exams below this---
v2020
k2020
v2021
k2021
v2022
k2022
v2023		D

Pugg

Spørretime

Må kunne følgende fordelinger:

• Laplace distribution
  • $f(x;\lambda )=\frac{\lambda }{2}\exp (-\lambda |x|)$
    • $\mathbb{E}\{X\}=0$
• Normal distribution
  • $f(x;\mu ,\sigma )=\frac{1}{\sqrt{2\pi {\sigma }^2}}\exp \left(-\frac{(x-\mu {)}^2}{2{\sigma }^2}\right)$
    • $\mathbb{E}\{X\}=\mu$
• Exponential distribution
  • $f(x;\lambda )=\lambda \exp (-\lambda x)u(x)$
    • $\mathbb{E}\{X\}=\frac{1}{\lambda }$
• Uniform Distribution
  • $f(x;a,b)=\frac{1}{b-a},x\in [a,b]$
    • $\frac{a+b}{2}$

BLUE

MLE Classical Version MAP Bayesian version

Les BMMSE og MAP

Mye “bevis at” oppgaver.

• Lettere å motbevise enn å bevise

ML, MVU og BLUE og deres forhold

Konfidensintervall

Estimation

$$\frac{\partial \log p(x;\theta )}{\partial \theta }=I(\theta )(g(x)-\theta )$$

• $\hat{\theta }=g(x)$
• $var(\hat{\theta })=I^{-1}(\theta )$

Detection

Bayes Decision Rule Bayesian Detection Neyman-Pearson Theorem

Classification