1 / 9

Probability

Probability Definition : The probability of a given event is an expression of likelihood of occurrence of an event .A probability is a number which ranges from 0 to 1. 0 for an event which cannot occur 1 for an event which can occur.

yestin
Télécharger la présentation

Probability

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ProbabilityDefinition : The probability of a given event is an expression of likelihood of occurrence of an event .A probability is a number which ranges from 0 to 1. 0 for an event which cannot occur 1 for an event which can occur

  2. Importance for the concept of ProbabilityAccording to Ya-lun Chou : “Statistics as a method of decision- making under uncertainty, is founded on probability theory, since probability is at once the language and the measure of uncertainty and the risks associated with it .”

  3. Experiment : The term experiment refers to processes which result in different possible outcomes or observations.Random Experiment : 1) all possible outcomes are known in advance. 2) none of the outcomes can be predicted with certainty.

  4. Note :Each performance of a random experiment is called a Trialand the result of a performance ( or trial) is called an outcome or case.Sample Point : The outcome of the random experiment is called a sample point.Sample space :The set of all possible outcomes ( or sample points) of a random experiment is called a sample space.

  5. Finite Sample space : A sample space is said to be finite if it contains a finite number of sample points.Infinite Sample space : A sample space is said to be infinite if it contains a infinite number of sample points.Discrete Sample space:A sample space is said to be discrete if it contains finite or finitely many or countably infinite sample points which can be arranged into a simple sequence E1,E2…….. Corresponding to natural number.

  6. Continuous Sample space :A sample space is said to be continuous if it contains non-denumerable(uncountable) number of sample points.Events: A subset of a sample space is called an event. An empty subset φ of S us called impossible event and the space itself is called a certain event.The subset containing a simple sample point is known as simple event or elementary event.

  7. Types of event Equally like Events : Two or more events are said to be equally likely if any one of them can not be expected to occur in preference to the others.Example: In a tossing of an unbiased coin, Head is likely to come up as tail.Composite Event : The union of two events A & B denoted by A U B and A + B is called a composite event of A & B.

  8. Compound Event: The intersection of two events A & B denoted by A∩B or AB is called compound event of A & B.Mutually Exclusive ( or Incompatible) Events : Two events are said to be mutually exclusive if they have no sample point in common i.e. A∩B =ФExhaustive events : Two events are exhaustive if their union is equal to the sample space.Independent Events: Two or more events are said to be independent if the occurrence of one does not affect the occurrence of the other.

  9. Dependent Events : Two events are said to be dependent if the occurrence of one affects the occurrence of the other.Mutually exclusive & Exhaustive Events : A number of events are said to be mutually exclusive & exhaustive events if i) every two of them are mutually exclusive ii)one of them necessarily occurs in any trial.

More Related