Understanding Mutually Exclusive and Independent Events in Probability Theory, Study notes of Statistics

Definitions and explanations of mutually exclusive and independent events in probability theory. Mutually exclusive events are those which cannot occur at the same time, while independent events have probabilities that are not affected by each other. Additionally, the concepts of random variables and distribution functions are introduced.

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2011/2012

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Event :
Two events are said to be mutually exclusive events if and only if they
can not both occur together at the same time. OR Two events are said to
be mutually exclusive events if the occurrence of one event discard the
occurrence of other event.
Independent
events :
Two events A and B in the same sample space S, are defined to be
independent (or statistically independent) if the probability that one event
occurs, is not affected by whether the other event has or has not occured.
Random
variable :
A numerical quantity whose value is determined by the outcome of a
random experiment is called a random variable.
Distribution
Function :
The function which gives the probability of the event that X takes a value
less than or equal TO a specified value x is called a distribution function
and is also called the cumulative distribution function.
Cumulative The function which gives the probability of the event that X takes a value
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Event :Two events are said to be mutually exclusive events if and only if theycan not both occur together at the same time. OR Two events are said tobe mutually exclusive events if the occurrence of one event discard theoccurrence of other event.Independentevents :Two events A and B in the same sample space S, are defined to beindependent (or statistically independent) if the probability that one eventoccurs, is not affected by whether the other event has or has not occured.Randomvariable :A numerical quantity whose value is determined by the outcome of arandom experiment is called a random variable.DistributionFunction :The function which gives the probability of the event that X takes a valueless than or equal TO a specified value x is called a distribution functionand is also called the cumulative distribution function.Cumulative The function which gives the probability of the event that X takes a value