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?