Posted On : 16.07.2018 03:22 am

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

**Probability Density Function**

The probability function associated with continuous random variable is called probability density function.

**Probability
mass function and probability density function**

A probability function is associated with each value of the
random variable. This function is used to compute probabilities for events
associated with the random variables. The probability function defined for a
discrete random variable is called probability mass function. The probability
function associated with continuous random variable is called probability density
function.

**Probability
Density Function**

When the random variable is continuous in the co-domain it is
spread over it. A function *f* (*x*) is defined on real line and
satisfying the following conditions :

is called the probability density function(p.d.f) of X.

** **

**Example 9.10**

A continuous
random variable *X* has probability density function given by

*Solution:*

** **

**Example 9.11**

Verify
whether the following function is a probability density function

*Solution:*

** **

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11th Statistics : Chapter 9 : Random Variables and Mathematical Expectation : Probability Density Function |