Posted On : 16.07.2018 04:38 am

## Chapter: __11th Statistics : Chapter 9 : Random Variables and Mathematical Expectation__

**Distribution function and its properties**

i. Distribution Function for discrete random variable
ii. Distribution Function for continuous random variable

**Distribution
function and its properties**

We
get the probability of a given event at a particular point. If we want to have
the probability upto the point we get the probability *P*(*X*
≤ *x*). This type of probability is known as probability mass
function. We can also find how the probability is distributed within certain
limits. [*P* (*X* < *x*) or *P* (*X* > *x*) or *P* (*a* < *x* < *b*)].

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**Distribution
Function for discrete random variable**

Definition:
Let *X* be a random variable ,the cumulative distribution
function (c.d.f) of a random variable *X* is defined as *F*(*x*)
= *P*(*X*≤*x*), 6*x*. It is called simply as
distribution function.

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**Properties:**

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**Distribution
Function for continuous random variable**

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**Properties**

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**Example 9.12**

A
random variable *X* has the following probability
mass function

i.
Find the value of ‘*a ’*

ii.
Find the c.d.f *F*(*x*) of *X*

iii.
Evaluate : (a) *P*(*X*
≥ 4) (b) *P*(*X* < 5) (c) *P*(3 ≤ *X* ≤6)

*iv. P*(*X *= 5) using* F*(*x*)

*Solution:*

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**Example 9.13**

Let
*X* be a random variable with p.d.f

*Solution:*

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Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

11th Statistics : Chapter 9 : Random Variables and Mathematical Expectation : Distribution function and its properties |