Differential Calculus

Differential Calculus

1. Basic Probability Concepts: Outcome is the possible result of the experiment, Sample Space is all possible outcomes, Event is any such subset of the sample, Experiment is any observation of a random phenomenon

   • Odds is compares to the number of favorable outcomes to the number of unfavorable outcomes
   • Probability FAormulas
     • Theoretical Probability Formula is P(E)=(number of favor outcome/ total number of outcome)
     • P(E)=(number of times the event E happened/number of times the Exp was performed)

2. Events involving "not" and "or"

   • Probability of the complement is P(not E)= 1-P(E)
   • Addition Rule is P(A or B)=P(A)+P(B)-P(A and B)
     • Mutually Exclusive is P(A or B)=P(A)+P(B)
   • Properties of Probability
     • Certain Event is P(S)=1
     • Imposible Event is P(0)=0
     • Probability Value is 0=P(E)=1

3. Events involving "and"

   • for any 2 events is P(A and B)= P(A)*P(A/B)
   • for independent events is P( A and B)=P(A)*P(B)
   • conditional probability formula is P(B)=P(A and B)/P(A)

4. Set Operations

   • Intersection is AnB=(xlx EA and EB)
   • Complement is A=(xlxEu and xEA)
   • Diference is A-B=(xlx EA and xEB)
   • Union is AuB=(xlx EA or xEB)

5. Ashraf Gad A01400386