# Lecture 3 – Random Variables

by Suraj Rampure (Summer 2020)

- slides
- video playlist
- Lecture Recap 1, Part 1 (video) (notes)

Make sure to complete the Quick Check questions in between each video. These are ungraded, but it’s in your best interest to do them.

Video | Quick Check | |
---|---|---|

3.1 Formal definition of random variables. |
3.1 | |

3.2 Distributions of random variables. |
3.2 | |

3.3 Defining the Bernoulli and binomial distributions. (Stat 88 reading) |
3.3 | |

3.4 Discussing equality of random variables – equal vs. equal in distribution. |
3.4 | |

3.5 Expectation. Linearity of expectation. Sample calculations, and the expectation of the Bernoulli and binomial distributions. |
3.5 | |

3.6 Variance of random variables. Walking through an alternate calculation of variance. Variance of a linear transformation. |
3.6 | |

3.7 Deriving the variance of a sum. Understanding covariance, correlation, and independence. |
3.7 | |

3.8 Variance of an i.i.d. sum. Variance of the Bernoulli and binomial distributions. |
3.8 | |

3.9 Variability of the sample mean. Reviewing inferential concepts from Data 8, but with the framework of random variables. |
3.9 |