Cálculo Diferencial - Module 1. Probability and statistics.

Cálculo Diferencial - Module 1. Probability and statistics.

1. Alejandro Baruch Saucedo Esparza - A01400284

   • Lic. Saul Garcia

2. Probability and statistics

   • 1.1Probability Basic Concepts
     • Deterministic Phenomenon: It can be predicted exactly on the basis of obtainable information
     • 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
   • Events Involving "NOT" and "OR"
     • 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)
     • 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)
   • Events Involving and
     • 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)
     • Conditional Probability formula (of B given A)
     • 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)
   • Venn Diagrams
     • 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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