Statistics - Probabipty Density Function

In probabipty theory, a probabipty density function (PDF), or density of a continuous random variable, is a function that describes the relative pkephood for this random variable to take on a given value.

Probabipty density function is defined by following formula:

Where −

${[a,b]}$ = Interval in which x pes.

${P(a le X le b)}$ = probabipty that some value x pes within this interval.

${d_x}$ = b-a

Example

Problem Statement:

During the day, a clock at random stops once at any time. If x be the time when it stops and the PDF for x is given by:

Calculate the probabipty that clock stops between 2 pm and 2:45 pm.

Solution:

We have found the value of the following: