Calculus Map

Calculus Map

1. Basic Concepts

   • Event
     • Any such subset of the sample space
   • Outcomes
     • The possible results of a certain experiment
   • sample space
     • Set of all posible outcomes
   • Experiment
     • Any observation or measurement on a random phenomenon

2. Venn Diagrams

   • Set Operations
     • COMPLEMENT
       • A´={xIx E U and x E A}
     • INTERSECTION
       • A^B{xIx E A or x E B}
     • UNION
       • AUB{xIx E A or x E B}
     • DIFFERENCE
       • A-B={(x,y)Ix A and y E B}

3. Odds

   • Compare the number of favorable outcomes to the number of unfavorable outcomes

4. Probability Formulas

   • Empirical Probability
     • P(E)= Number of times event E occurred/ Number of times the experiment was performed
   • Theorical Probability
     • P(E)= Number of favorable outcomes/ Total number of outcomes

5. Events

   • OR
     • Addition Rule of Probability
       • If A and B are only 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 and B)=P(A)+P(B)
           • Mutually Exclusive Events:
             • two events A and B are mutually exclusive if they have no outcomes in common
               • P(A or B)=P(A) + P(B)
   • NOT
     • Properties
       • Certain Event
         • Dividing all members of this inequality by n(s) gives. 0<n(E)<n(s)
       • Probability Value
         • A number from 0 through 1
       • Impossible Event
         • If E is impossible then n(e) must be 0, (e) is the empty set so P(E)=0
   • AND
     • Conditional Probability Formula
       • P(B/A)=P(A^B)/P(A)
         • IGUAL A: P(A and B)/P(A)
           • Conditional Probability of B given A
     • Multiplication Rule Of Probability
       • For independent events
         • P(A and B)= P(A)x P(B/A)
       • For any tow events
         • P(A and B)= P(A)xP(B)
   • Probability of the Complement
     • The probability that an event E will not occur is the equal to one minus the probability that it will occur