Products
Rewards
from HOLOOLY

We are determined to provide the latest solutions related to all subjects FREE of charge!

Enjoy Limited offers, deals & Discounts by signing up to Holooly Rewards Program

HOLOOLY

HOLOOLY
TABLES

All the data tables that you may search for.

HOLOOLY
ARABIA

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

HOLOOLY
TEXTBOOKS

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

HOLOOLY
HELP DESK

Need Help? We got you covered.

## Q. 2.9

Use the Dirac delta function to write an expression for the probability density function of the discrete random variable X of Examples 2.1 and 2.4, having

$P (X=1) = P (X=2) = P (X=3) = P (X=4) = P (X=5) = P (X=6) = 1/6$

This probability density function can be written as

## Verified Solution

Strictly speaking, $\delta (\cdot )$ is not a function, but it can be thought of as a limit of a sequence of functions, as considered in Appendix A.

$p_{X} (u) =\frac{1}{6} [\delta (u-1) + \delta (u-2)+\delta (u-3)+\delta (u-4)+\delta (u-5)+\delta (u-6)]$

This expression is exactly the formal derivative of the cumulative distribution function in Example 2.4.