User:Azeari/Sandbox

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Contents

[edit] Master of Mathematical Science

To Date

  • ANOVA
  • multiple linear regression
  • Markov chains
  • queueing processes (exponential, poisson)
  • multivariate calculus
    • partial derivatives
    • double- and triple-integrals
    • div, grad & curl
  • Fourier analysis

Yet to do

  • parametric estimation using Maximum Likelihood (MAB414)
  • Inner Products: Gram-Schmidt Process and QR-Decomposition (MAB312)
  • Eigenvalues and Eigenvectors
  • Bayesian inference (MAB524)
  • Simulation techniques in S-Plus
  • generalized linear models (GLM)
  • Exponential smoothing, seasonal ARIMA models; long-range dependence and fractional ARIMA models (MAN526)
  • hidden Markov models and inference (MAN766)
  • ARCH models and inference

[edit] Equations and other miscellany

\mathbf{P} = \begin{bmatrix} 0.5 & 0.4 & 0.06 & 0.04 \\ 0.5 & 0.4 & 0.06 & 0.04 \\ 0 & 0.5 & 0.4 & 0.1 \\ 0 & 0 & 0.5 & 0.5 \end{bmatrix}

So therefore \pi_1 = {1 \over 2.64} = \pi_0

Let 0, 1 denote being absent ill from work, and not being absent. \mathbf{P} = \begin{bmatrix} 0.1 & 0.9 \\ 0.01 & 0.99 \end{bmatrix}

So 0.01π1 = (1 − 0.1)π0 {0.01 \over 0.9}\pi_1 = \pi_0 {1 \over 90}\pi_1 = \pi_0

({1 \over 90} + 1)\pi_1 = 1

\pi_1 = {90 \over 91}

\pi_0 = {1 \over 91}

\mathbf{P} = \begin{bmatrix} 0.01 & 0.18 & 0.81 \\ 0.001 & 0.108 & 0.891 \\ 0.0001 & 0.0198 & 0.9801 \end{bmatrix}

E(X) = \int_{10}^{\infty} x {200 \over x^3} dx

= \begin{bmatrix} {-200 \over x} \end{bmatrix}_{10}^{\infty}

= 0 - {-200 \over 10}

\int_{10}^{m} {200 \over x^3} dx = \int_{m}^{\infty} {200 \over x^3} dx = 0.5

\begin{bmatrix} {-100 \over x^2} \end{bmatrix}_{m}^{\infty} = 0.5

0 - ({-100 \over m^2}) = {1 \over 2}

100 = {m^2 \over 2}

\int_0^m f(x) dx = \int_m^{\infty} f(x) dx = 0.5

\int_0^1 { 12x^3 \over 7} dx + \int_1^m {12 \over 7x^4} dx = 0.5

\begin{bmatrix} {3x^4 \over 7} \end{bmatrix}_{0}^{1} + \begin{bmatrix} {-4 \over 7x^3} \end{bmatrix}_{1}^{m} = 0.5

{3 \over 7} - 0 + (-{4 \over 7m^3} + {4 \over 7}) = 0.5

{4 \over 7} - {4 \over 7m^3} = {7 \over 14} - {6 \over 14}

-{4 \over 7m^3} = -{7 \over 14}

4 = {7 \over 2}m^3

{8 \over 7} = m^3

m = \sqrt[3]{8 \over 7}

E(X) = \int_0^1 x {12x^3 \over 7} dx + \int_1^{\infty} x {12 \over 7x^4} dx

= \begin{bmatrix} {12x^5 \over 35} \end{bmatrix}_{0}^{1} + \begin{bmatrix} -{6 \over 7x^2} \end{bmatrix}_{1}^{\infty}

= {12 \over 35} - 0 + (0 - (-{6 \over 7}))

= {12 + 30 \over 35}

E(x^2) = \int_0^1 x^2 {12x^3 \over 7} dx + \int_1^{\infty} x^2 {12 \over 7x^4} dx

= \begin{bmatrix} {2x^6 \over 7} \end{bmatrix}_0^1 + \begin{bmatrix} -{12 \over 7x} \end{bmatrix}_{1}^{\infty}

= {2 \over 7} - 0 + (0 - (-{12 \over 7}))

= {14 \over 7} = 2

E(X2) − μ2 = 2 − 1.22 = 0.56years2

[edit] Mercedes Cortez

Mercedes Cortez
Enlarge
Mercedes Cortez

Mercedes Cortez is Juan's wayward daughter. She is initially set up as a possible love interest for Tommy Vercetti, but this plotline is never explored. Tommy is first introduced to her during a party aboard the Colonel's yacht. Afterwards, she asks Tommy to give her a ride to the Pole Position strip club. On another occasion, she parties with the band Love Fist. Later in the game, she becomes involved in the porn film industry, co-starring with Candy Suxxx in a film directed by Steve Scott and produced by Vercetti.

Mercedes Cortez was voiced by Fairuza Balk

Matt

[edit] Petrea

iPetrea
Scientific classification
Kingdom: Plantae
Division: Magnoliophyta
Class: Magnoliopsida
Order: Lamiales
Family: Verbenaceae

The Petrea is an evergreen flowering vine.

Known species include:

  • Petrea volubilis

[edit] Angola

Not sure where 198.96.37.124 got the reference (LeBillon, 1999) from - his Ph.D. thesis? I think we need a better reference to the works of Dr Philippe Le Billon ...perhaps his recent book.

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