L2 Bernoulli Sequences
1- It was narrated that Abu Hurairah said: “One of the supplications that the Prophet used to say was:
اللَّهُمَّ إِنِّي أَعُوذُ بِكَ مِنْ عِلْمٍ لَا يَنْفَعُ وَمِنْ دُعَاءٍ لَا يُسْمَعُ وَمِنْ قَلْبٍ لَا يَخْشَعُ وَمِنْ نَفْسٍ لَا تَشْبَعُ
[0 Allah, I seek refuge with You from knowledge that is of no benefit, from a supplication that is not heard, from a heart that does not fear (You) and from a soul that is not satisfied].’”
(Sunan Ibn e Majah, Book of Sunnah, Hadith no 250, Classified as Sahih By Allama Albani)
2- It was narrated that Abu Hurrairah said: “The Messenger of Allah used to say:
اللَّهُمَّ انْفَعْنِي بِمَا عَلَّمْتَنِي وَعَلِّمْنِي مَا يَنْفَعُنِي وَزِدْنِي عِلْمًا وَالْحَمْدُ لِلَّهِ عَلَى كُلِّ حَالٍ
[0 Allah, benefit me by that which you have taught me, and teach me that which will benefit me]
(Sunan Ibn e Majah, Book of Sunnah, Hadith no 251)
Intro Stats: Islamic Approach: Part 2: Probability and Statistics
Lecture 2: Bernoulli Sequences
A random variable is obtained by looking at some characteristic of a random draw from a population. For example, after picking one person randomly, we look at his/her age, or gender, or nationality, or weight. These are all random variables. A BERNOULLI random variable is obtained when the characteristic is BINARY -- it has only two possible values. For example GENDER, male or female, would qualify as a BINOMIAL. In such cases, it is customary to code one of the cases as "1" and the other as "0"; this coding makes the outcome of the random variable numeric, which is very convenient for many different kinds of algebraic manipulations.
CONCEPTS COVERED IN THIS LECTURE:
3: Multiplication Law for Dependent Events
4: Computing Probabilities for Bernoulli Sequences
5: Differentiating Between Pre and Post Experimental Concepts
Omar Khayyám (c. 1038/48 in Iran – 1123/24)[9] wrote the Treatise on Demonstration of Problems of Algebra containing the systematic solution of cubic or third-order equations, going beyond the Algebra of al-Khwārizmī.[10] Khayyám obtained the solutions of these equations by finding the intersection points of two conic sections. This method had been used by the Greeks,[11] but they did not generalize the method to cover all equations with positive roots.[12]
Sharaf al-Dīn al-Ṭūsī (? in Tus, Iran – 1213/4) developed a novel approach to the investigation of cubic equations—an approach which entailed finding the point at which a cubic polynomial obtains its maximum value. For example, to solve the equation
, with a and b positive, he would note that the maximum point of the curve occurs at , and that the equation would have no solutions, one solution or two solutions, depending on whether the height of the curve at that point was less than, equal to, or greater than a. His surviving works give no indication of how he discovered his formulae for the maxima of these curves. Various conjectures have been proposed to account for his discovery of them.[13
Hadeeth & Ayat on Seeking Knowledge
Wikipedia Entry — Excerpt on Omar Khayyam and Al-Tusi