List of Formulae and Definitions of Probability and Random Process

LIST OF FORMULAE AND DEFINITIONS :

1. P(A) = Favourable number of cases/Exhaustive number of cases = n(A)/n(S) = m/n, 0 ≤ P(A) ≤ 1

2. Probability (impossible event): 0 (i.e.,) P(φ) = 0

3. P(Ā) = 1 - P(A)

4. Three types of Events

6. P (A/B) means that the conditional probability of A given by B.

7. Two independent events can not be mutually exclusive.

8. Two possible mutually exclusive events are always dependent.

9. The advantage of the axiomatic theory is that it narrates all situations irrespective of whether the outcomes of an experiment are "equally likely" or not.

10. P(A/A) = 1

11. If A and B are independent, their complements Ā and eeeeeeee B are also independent.

12. The probability of

13. Marginal probability: "The probability of only one event that taken at a time when both are occurring jointly is called "Marginal Probability".

14. Joint probability: The probability of occurrence of both the events A and B together, denoted by P (A∩B), is known as joint B), is probability of A and B.

15. Conditional probability: The conditional probability of A for the given B is P (A/B) = P(A∩B)/P(B) if P(B) ≠ 0 and it is undefined if P(B) = 0.

A rearrangement of the above definition yields the following:

MR (Multiplication Rule)

16. Explain the term "two events are independent".

Two events are independent if any one of the following equivalent statements is true.

i. P(A/B) = P(A) ii. P(B/A) = P(B) iii. P(A∩B) = P(A) P(B)

17. Type of Random variables:

i. Discrete random variables

ii. Continuous random variables