__Chapter 02 Highlights and Questions (II)__

Points for discussion (section 2.5 - 2.8)

- Page 49: definition of categorical and multinomial distributions
- Page 50: softmax function and logit
- Page 51: why it is called softmax function?
- Page 53: definition of univariate Gaussian distribution?
- Page 54: definition of the Student t distribution?
- Page 59:
- definition of Laplace distribution
- definition of Beta distribution

- Page 60: the shape of Beta cdf with respect to different values of \( \alpha \) and \( \beta \)
- Page 62: change of variables
- Page 67: central limit theorem
- Page 68: Monte Carlo approximation

Questions for section 2.5 - 2.8

- In section 2.5.2, what is a logit? Why the function \( \frac{\exp(f_c(x))}{\sum_{c’}f_{c’}(x)} \) is called softmax function?
- Why is the Gaussian distribution so widely used?
- How to compute the expeced value of a continuous random variable, given the probability density function?
- What the applications of the change of variables formula?
- How to use Monte Carlo approximation to compute the expected value of a random variable, when the exact computation is intractable?