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

Probability density function is defined by following formula:

Where −

- ${[a,b]}$ = Interval in which x lies.
- ${P(a \le X \le b)}$ = probability that some value x lies 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:

\begin{cases}

1/24, & \text{for $ 0 \le x \le 240 $} \\

0, & \text{otherwise}

\end{cases} }$

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

**Solution:**

We have found the value of the following:

\ = \frac{1}{24} (14.45 – 14) \\[7pt]

\ = \frac{1}{24}(0.45) \\[7pt]

\ = 0.01875 }$

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