Sumários
Two dimensional discrete and continuous random variables. Conditional probabilility and density probability functions.
24 Outubro 2014, 15:30 • Graça Leão Fernandes
Pg. 90- nºs: 3.42, 3.43, 3.44, 3.45, 3.49, 3.50, 3.51
from exercises for Chapter 2: nºs 26, 30, 34, 36
Conditional probability functions. Two dimensional continuous random variables.
21 Outubro 2014, 13:30 • Graça Leão Fernandes
Discrete two dimensional random variables:
- Conditional probability functions of X given Y and Y given X and their properties.
Continuous two dimensional random variables:
- Definition;
- Joint probability density function and its properties;
- Marginal probabilitydensity function of X and Y;
- Joint cumulative distribution function;
- Marginal cumulative distribution function of X and Y;
- Independence of two dimensional continuous random variables;
- Conditional probability density functions of X given Y and Y given X and their properties.
- Examples.
Two dimensional random variables. Discrete two dimensional random variables..
20 Outubro 2014, 13:30 • Graça Leão Fernandes
Two dimensional random variables:
- Definition;
- Joint cumulative distribution function and its properties;
- Independence of two dimensional random variables.
- Marginal cumulative distribution function of X and Y.
Discrete two dimensional random variables:
- Definition;
- Joint probability function and its properties;
- Marginal probability function of X and Y;
- Joint cumulative distribution function;
- Marginal cumulative distribution function of X and Y;
- Independence of two dimensional discrete random variables;
- Examples.
Continuous random variables. Functions of random variables.
17 Outubro 2014, 15:30 • Graça Leão Fernandes
Solving exercises
Book: pg. 80 nºs 3.17, 3.22, 3.28
pg. 81 nºs 3.38, 3.41
From Exercises for Chapter 2 nºs: 7c), 12, 13a), 14, 22 c)
Functions of random variables.
14 Outubro 2014, 13:30 • Graça Leão Fernandes
Functions of random variables - random variable Y is a function of random variable X.
The distribution function technique: finding the cdf of random variable Y knowing the cdf of random variable X
- case when random variable X is discrete;
- case when random variable X is continuous and random variable Y are both continuous
- Y is an increasing function of X
- Y is an decreasing function of X;
- case when random variable X is continuous and random variable Y is mixed;
- case when random variable X is continuous and random variable Y is ciscrete;