Bivariate Sampling Statistics

Bivariate Sampling Statistics

Versión en Español
Colección de JavaScript Estadísticos en los E.E.U.U.
Sitio Espejo para América Latina

This site is a part of the JavaScript E-labs learning objects for decision making. Other JavaScript in this series are categorized under different areas of applications in the MENU section on this page.

Professor Hossein Arsham   

Enter (by replacing) your up-to-42 two samples paired-data sets where measurements are made jointly on two random variables (X, Y) per subject, and then click the Calculate button. Blank boxes are not included in the calculations but zeros are.

In entering your data to move from cell to cell in the data-matrix use the Tab key not arrow or enter keys.

Risk Assessment Process: Clearly, different subjective probability models are plausible they can give quite different answers. These examples show how important it is to be clear about the objectives of the modeling. An important application of subjective probability models is in modeling the effect of state-of-knowledge uncertainties in consequence models. Often it turns out that dependencies between uncertain factors can be important in driving the output of the models. For example, consider two portfolios having random X and Y returns; the ratio:

Cov(X, Y) / Var (X)

is called the beta of the random variable X with respect to Y. Various methods are available to model these dependencies, in particular proportional to the Beta values methods.

Buying Gold or Foreign Currencies Investment Decision: Suppose you observed and then obtained the join trading returns of the following two investments, over say, 5 (equally-spaced) periods , the join random rate of returns are tabulated below:

Join Trading Random Rate of Returns for C and G
Currencies (C) 5 -1 3 4
Gold (G) 2 5 4 3

Given you wish to invest $12,000 over one period (with the same length of time), how do you invest for the optimal strategy?

Using the JavaScript we obtain:

Beta (Currencies) = -0.4578313,    and     Beta (Gold) = -1.9

Now, one may distribute the total capital ($12000) proportional to the Beta values:

Sum of Beta’s = -0.4578313 -1.9 = -2.3578313

12000 (-0.4578313 /-2.3578313) = 12000(0.1941747) = $2330 ,   Investing on Foreign Currencies

12000 (-1.9/-2.3578313) = 12000(0.8058253) = $9670,   Investing on Gold

That is, the optimal strategic decision based upon the Beta criterion is:

Buy $2330 foreign Currencies,    and    $9670 Gold.

Notice that Beta1 and Beta2 are directly related, for example, the multiplication of the two provides the correlation square, i.e. r2. The r2 which always between [0, 1] is a number without any dimensional units, and it represent strong is the linear dependency between the rates of return of one portfolios against the other one. When any beta is negative, and the r2 is large enough, then the two portfolios are related inversely and strongly. In such a case, diversification of the total capital is recommended.

Variable X
Variable Y
Variable X
Variable Y
Variable X
Variable Y
Mean(X) Mean(Y)
Variance(X) Variance(Y)
Covariance (X, Y) Correlation (X, Y)
Beta(X) Beta(Y)

For Technical Details, Back to:
Zero-Sum Games with Applications

Kindly email your comments to:
Professor Hossein Arsham

Muestreo Estadístico de Doble Variación
Nota para los usuarios de habla hispana:
Introduzca hasta 42 pares de datos muestrales donde las mediciones son hechas sobre dos variables aleatorias (X, Y) por caso, y luego presione el botón Calculate (Calcular). Los espacios en blanco no son asumidos como ceros ni incluidos en los cálculos, pero los números cero si se incluyen. Esta matriz reconoce al punto (.) como el signo decimal en vez de la coma (,).
Mientras entre sus datos en la matriz, muévase de celda a celda usando la tecla Tab, no use la flecha o la tecla de entrada.
Los resultados que usted obtendrá de esta matriz son:
Mean (X) = Media (X)
Mean (Y) = Media (Y)
Variance (X) = Varianza (X)
Variance (Y) = Varianza (Y)
Covariate (X, Y) = Covarianza de (X, Y)
Para Detalles Técnicos y Aplicaciones, Vuelta a:
Razonamiento Estadístico para la Toma de Decisiones Gerenciales


Decision Tools in Economics & Finance

Probabilistic Modeling


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Kindly e-mail me your comments, suggestions, and concerns. Thank you.

Professor Hossein Arsham   

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Dr Arsham's Home Page

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