Sumários

Lecture 15

15 Abril 2024, 12:00 Davide Masoero

k-dimensional random variable
Expected value of the sum, variance of the sum and moment generating function of the sum of k random variable
Independent and identically distributed (i.i.d) random variables
Chapter 6
Discrete uniform distribution
Bernoulli distribution
Binomial distribution
Exercise and use of the numerical table


Practice 8

12 Abril 2024, 10:30 Ricardo Pinto Moura

Chapter 4: 13

Chapter 5: 1, 2, 5, 7


Lecture 14

10 Abril 2024, 13:30 Davide Masoero

Review: expected value of a function of a bidimensional random variable.
Covariance, definition and properties.
Variance of  a function of a bidimensional random variable.
Variance of the sum of random variable and covariance.
Exercise 5 of Chapter 5.
Linear correlation coefficients. Scatter plots.
Conditional Expectation, conditional mean, mean independence. Example.
Law of iterated expectations. Example: average gross salary by education level


Lecture 13

8 Abril 2024, 12:00 Davide Masoero

Review: bidimensional continuous random variable
Expected values of a function of a two-dimensional random variable.
Expected value of the sum of two random variables and expected value of the product of two independent random variable.
Exercise.
Product moments about the origin and about the mean. Case when r+s= or r+s=2.
Covariance. Properties, Cov (X,Y)= E[X Y]-E[X] E[Y]


Practice 7

5 Abril 2024, 10:30 Ricardo Pinto Moura

Chapter 4: 4; 5; 8; 11