## Important Disclaimers

##### There is some important history to the “taf” (taasia venihul) and “mem” (murchevet) in Histabrut “taf” and “mem”.

When the slides below were prepared, and when the video for “Histabrut Mem” was made, there was only one course, called “Histabrut Mem”. After the subject was split into two, the new “Taf” was much closer to the old “Mem” than the new “Mem” is.

In other words, if you rely on my video and my slides for “Histabrut Mem” and you end up failing, *DON’T BLAME ME *.

In fact, even if you are taking “Histabrut Taf”, the course has changed somewhat since the video was made, and there *IS NO SUBSTITUTE FOR GOING TO LIVE LECTURES.*

**HAVE YOU PASSED HEDVA 2 OR 2 MEM YET?**

If not, then you are technically not eligible to enrol in Histabrut. Policy regarding this will be given in the first lecture of the semester.

However, whatever the case, you may want to look at this , kindly given to us by Tomer Galler, who obviously thoroughly enjoyed learning Calculus.

**DOWNLOADABLE LECTURES FOR MY (ADLER’S) CLASSES ONLY:**

The slides below lectures are for the Spring Semester of the 2008/2009 academic year.

They contain significant changes to earlier versions and are different in order and substance to those used in the video of the course.

NOTE: There will be more material in lectures that what is written on the slides, which are themselves incomplete and need to be annotated by students in lectures. DO NOT RELY only on these slides to pass the course.

Lecture | Topics |
---|---|

1 | Four problems in probability, probability spaces, axioms… |

2 | Probability spaces, equally likely outcomes… |

3 | Conditional probability, multiplication rule…. |

4 | Law of total probability, Bayes’ rule, sequences of events…. |

5 | The birthday problem, gamblers ruin, Polya’s urn…. |

6 | Non-uniform spaces, biased coins, geometric distribution…. |

7 | Repeated trials, binomial distribution, approximations…. |

8 | Sampling…. |

Wombats | You need to know about these for lecture 9. |

9 | Poisson distribution, Poison process, exponential distribution…. |

10 | Random variables, distributions, functions of random variables…. |

11 | Bivariate, marginal and conditional distributions. Independence…. |

12 | Order statistics, random permutations…. |

13 | Multinomial distribution, conditional independence…. |

14 | Expectation, measures of centrality…. |

15 | More on expectation. Boole and Markov inequalities…. |

16 | Expectation of a function, multiplication rule, prediction…. |

17 | Variance, standard deviation, Chebychev’s inequality…. |

18 | Covariance, correlation…. |

19 | Correlations, Sharkey’s casino, variance of sum…. |

20 | Laaws of large numbers, random walk, large deviations…. |

21 | Moment generating functions, sums of random variables…. |

22 | Probability densities, infinitessimals…. |

23 | Normal distribution, central limit theorem…. |

24 | Central limit theorem and applications….. |

25 | Exponential distribution, gamma distribution, lack of memory…. |

26 | Distribution functions….. |

27 | Maxima and minima, percentiles, simulation theorem…. |

28 | Transformations of continuous random variables…. |

29 | Continuous joint distributions, marginals….. |

30 | Independence of continuous random variables, order statistics…. |

31 | Discrete conditional distributions, conditional expectation…. |

32 | Conditional expectations, conditional densities…. |

33 | Continuous Bayes’ theorem, random sums…. |

34 | Coniditional variance, random sums, convolution of densities… |

35 | Transformations…. |

36 | Multivariate normal distribution, covariance matrices…. |

37 | Multivariate normal, regression to the mean, simulation of normals…. |

38 | More on the multivariate normal.. |