Cálculo Diferencial - Module 1. Probability and statistics.

Alejandro Baruch
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Alejandro Baruch
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Modulo 1, mini proyecto.

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Cálculo Diferencial - Module 1. Probability and statistics.
1 Alejandro Baruch Saucedo Esparza - A01400284
1.1 Lic. Saul Garcia
2 Probability and statistics
2.1 1.1Probability Basic Concepts
2.1.1 Deterministic Phenomenon: It can be predicted exactly on the basis of obtainable information
2.1.2 Random Phenomenon: It fluctuates in such a way that its value cannot be predicted exactly with obtainable information Probability Basic Concepts Outcomes Possible Results of the experiment Sample Space Set of all possible answers event Any subset of the sample space Experiments Observation or measurement of a random phenomenon Odds Compare the number of favorable outcomes with number of unfavorable outcomes. Ex: To get 1 in dais. 1 to 5 favorable outcomes, 5 to one unfavorable, 1/6 probabilities Probability Formulas Theoretical Formula Empirical Formula Converting between probability and odds Let E be an event If P(E)= a/b, then the odds in favor of E is (b-a) If the odds in favor of E are a to b, then P(E)=a/(a+b) Properties of Probability Let E be an event within the sample space (S). That is E a subset of S then the following properties hold Probability of value Impossible event Certain event
2.2 Events Involving "NOT" and "OR"
2.2.1 Probability of the complement Probability that on event E will not occur (Not E) is equal to 1 minus the probability that will occur. P(not E)=1-P(E)
2.2.2 Addition rule of probability If A and B are any two events then: P(A or B)=P(A) + P(B) - P(A and B). If A and B are mutually Exclusive then: P(A or B)= P(A)+P(B) Two events are mutually exclusive if they have no outcomes in common(can´t occur simultaneously)
2.3 Events Involving and
2.3.1 The probability of event B, Computed on the assumption that event A has happened, is called the conditional probability of B given A and is denoted P(A/B)
2.3.2 Conditional Probability formula (of B given A)
2.3.3 Multiplication rule of probability Independent events Two events are called independent events if the knowledge about the occurrence of one of them has no effect on the probability of the other one, that is, if P(B/A)=P(B), or equivalently, P(A/B)=P(A). (applies in all cases) P(A and B)=P(A)P(B) Any two events P(A and B)=P(A)P(B/A)
2.4 Venn Diagrams
2.4.1 Let A and B be any sets, with U the universal set. Complement The Complement of A, written A´, is: Intersection The intersection of A and B is Union The union of A and B is Difference The difference of A and B is Cartesian product The cartesian product of A and B is
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