Product moments about the origin and the mean for discrete and continuous two dimensional random variables. Covariance and correlation coefficient. conditional expected values.

12 Novembro 2015, 15:30 • Graça Leão Fernandes

Exercises from Chapter 3 nºs: 12, 14, 17, 19, 23

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Correlation coefficient. Conditional expected values of X and Y.Conditional variance.

11 Novembro 2015, 15:30 • Graça Leão Fernandes

Correlation coefficient:

- computation;

- interpretation.

Conditional expected values of X and Y for discrete and continuous two dimensional random variables:

- Conditional expected values of X given Y=y;

-  Conditional expected values of Y given X=x.

Conditional variance.

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Product moments about the origin and about the mean of order r+s for two dimensional random variables

9 Novembro 2015, 13:30 • Graça Leão Fernandes

Product moments about the origin of order r+s for two dimensional discrete and continuous random variables:

- Definition;

- case when r=1, s=1 E(X.Y);

- Expected value of a function of X and Y;

- Marginal expected values of X and Y - r=1, s=0  or r=0, s=1;

- Study of independence of X and Y based on the moments about the origin;

- Expected value of a linear combination of n random variables.

Product moments  about the mean of order r+s for two dimensional discrete and continuous random variables:

- case when r=1, s=1 Cov(X.Y)- computation and interpretation;

- covariance and independence;

- Marginal variance of X and Y;

-  Covariance of a linear combination of n random variables.

 

 

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Expected value and variance of discrete and continuous random variables. Moments about the origin and around the mean. Order statistics. Moment generating function.

29 Outubro 2015, 15:30 • Graça Leão Fernandes

Exercises of Chapter 3 nºs 1, 3, 4, 6, 7, 10

 

Realisation of the 2nd mini test

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Ex from chapter 3

29 Outubro 2015, 15:30 • Agnieszka Bergel

Ex from chapter 3, expected value, variance, median. Ex 1,3,4,6. 

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