Sumários
Properties of the Expected value and variance for two dimensional random variables.Correlation coeficient. Conditional expectations.
4 Novembro 2014, 13:30 • Graça Leão Fernandes
Properties of the expected value and variance for two dimensional random variables:
- Expected value of a sum of random variables;
- Variance of a sum of independent random variables;
- Covariance of a sum of independent random variables.
Correlation coeficient: definition, computation and interpretation;
Conditional expectations:
- Expected value of X given Y for discrete and continuous random variables;
- Expected value of Y given X for discrete and continuous random variables;
- Conditional Variance of X given Y for discrete and continuous random variables;
Product moments about the origin and about the mean for discrete and continuous random variables
3 Novembro 2014, 13:30 • Graça Leão Fernandes
Product moments about the origin of order r,s:
- Definition;
- Expected value of (X.Y), marginal expected values of X and Y;
- Theorem 4.12 - independence between X and Y
- Expected value of some functions of (X.Y)
Product moments about the mean of order r,s:
- Definition;
- Covariance of X,Y, interpretation;
- Variance of X and Y;
- Examples.
Expected values, moments of discrete and continuous random variables. Moment generating functions.
31 Outubro 2014, 15:30 • Graça Leão Fernandes
Resolution of exercises :
From the book: 4.6, 4.8, 4.19, 4.22, 4.24, 4.33, 4.34, 4.37
From exercises for chapter 3: 1,4, 5, 7, 10
Mini test nº 2
Order parameters. Moment generating function. Product moments about the origin.
28 Outubro 2014, 13:30 • Graça Leão Fernandes
Order parameters:
- Quantiles: Quartiles, deciles, percentiles;
Mode
Moment generating function:
- Definition;
- Properties;
- How to compute the moments about the origin using the mpment generating functions;
- Examples
Product moments about the origin:
- Definition:
- E(X,Y)
- E[g(X,Y)]
Expected values and moments of discrete and continuous random variables
27 Outubro 2014, 13:30 • Graça Leão Fernandes
Expected values:
- Definition;
- Computation for discrete and continuous random variables;
- Expected value of a function of X;
- Properties of expected values.
Moments of discrete and continuous random variables:
- Moments about the origin: definition, 1st and 2nd moments about the origin, interpretation;
- Moments about the mean: definition, 1st and 2nd moments about the mean, interpretation;
- Properties of the 2nd moment about the mean=variance;
- Standard deviation;
- Coefficient of variation;
- Coefficient of asymmetry;
- Coefficient of Kurtosis