Chapter: 11th Statistics : Chapter 9 : Random Variables and Mathematical Expectation
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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