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?