SHORT NOTES: Probability

Some Definition:

   Elementary Event(E):If a random experiment is performed then each of its outcomes is known as elementary event.

Sample Space(S):The set of all possible outcomes of a random experiment.

       Compound Event:A subset of sample space if it is disjoint union of single subsets of the sample space.
Mutually Exclusive Events:Occurrence of one event prevent the occurrence of others.

$P\left ( A\cap B \right )=0$

Independent Events: Occurrence of is not affected by occurrence of others.

Probability:

$P\left (A \right )=\frac{m}{n}$

n = total elementary events

m=events favorable to an event A

$0\leq P\left (A \right )\leq 1$

Addition and multiplication rules of probability:

Addition Theorem:

$P\left ( A\cup B \right )=P\left ( A \right )+P\left ( B \right )-P\left ( A\cap B \right )$

Multiplication Theorem :

$P\left ( A\cap B \right )=P\left ( A \right )P\left ( \frac{B}{A} \right )\\$ $P\left ( A \right )\neq0$

$P\left ( A\cap B \right )=P\left ( B \right )P\left ( \frac{A}{B} \right )\\$ $P\left ( B \right )\neq0$

Conditional probability:

$P\left ( \frac{A}{B} \right )$ : Probability of occurrence of A under condition that B has already occurred.

Baye's Rule:

$P\left( {{E_i}/A} \right) = \dfrac{{P\left( {{\rm{Darkly\, shaded \, region\,}}} \right)}}{{P\left( {{\rm{Total \,shaded \, region}}} \right)}}$

$= \dfrac{{P\left( {{\rm{A}} \cap {E_i}} \right)}}{{\sum\limits_{j{\rm{ = }}\,{\rm{1}}}^n {P\left( {A \cap {E_j}} \right)} }}$

$= \dfrac{{P\left( {{E_i}} \right)P\left( {A/{E_i}} \right)}}{{\sum\limits_{j{\rm{ = }}\,{\rm{1}}}^n {P\left( {{E_j}} \right)P\left( {A/{E_j}} \right)} }}$

${P\left( {{E_i}/A} \right) = \dfrac{{P\left( {{E_i}} \right)P\left( {A/{E_i}} \right)}}{{\sum\limits_{j = 1}^n {P\left( {{E_j}} \right)P\left( {A/{E_j}} \right)} }}}$

ELECTRICAL ENGINEERING
ENGINEERING MATHEMATICS	Electric Circuits and Fields
Signals and Systems	Electrical Machines
Power Systems	Control Systems
Electrical and Electronic Measurements	Power Electronics and Drives
Analog Electronics	Digital Electronics

Probability

No comments:

Post a Comment