Diferential Calculus map

Diferential Calculus map

1. Basic concepts

   • Event
     • When we have interest of a particular result.
   • Sample space
     • All possible outcomes
   • Experiment
     • Any observation or experiment on a random phenomenon
   • Outcomes
     • The possible results of certain experiment

2. Probability Formulas

   • Empirical Probability Formulas
     • P(E)= Number of times of the event/Number of times of the experiment
   • Theorical Probability Formulas
     • P(E): Favorable results/ Total results

3. Odds

   • See the number of favorable outcomes against the number of unfavorable outcomes

4. Events

   • Not
     • Properties of probability
       • Certain event
         • Dividing all the members of the inequality by n(s)
       • Impossible event
         • If E is impossible then n(e) must be zero (e) is empty so P(E)=0
       • Probability value
         • A number from 0 to 1
   • Or
     • Addition Rule of Probability
       • If A and B are mutually exclusive then: P(A and B)=P(A)+P(B)
         • Mutually exclusive events, If A and B have no common outcomes
           • P(A or B)=P(A)+P(B)
   • And
     • Multiplication rule of probability.
       • For any tow events
         • P(A and B)= P(A)xP(B)
       • For independent events
         • P(A and B)=P(A) x P(B/A)
     • Conditional probability formula
       • P(B/A)=P(A^B)/P(A)
         • =P(A and B)/P(A)
           • Conditional probability of B given A

5. Set Operations

   • Intersection
     • A^B[x/x E A or x E B]
   • Difference
     • A-B=[(x,y)/x A and y E B]
   • Union
     • AUB=[x/x E A or x E B]
   • Complement
     • A´=[x/xE U and x E A]