Random Variables

https://d2l.ai/chapter_appendix-mathematics-for-deep-learning/random-variables.html

Cauchy distribution is wrong, which should be image

18.6.31 is wrong by u=1+x^2

The second property of the correlation miss a sign(a)

Regarding Q3:
According to Chebyshev’s inequality:

image

Regarding Q4:

Ex2.


Ex3.

  • According to the Chebyshev Inequality,
    image
    therefore
    image
    The argument is therefore theoretically unbelievable.

Ex4.