# 4.1 Probability distribution function (pdf) for a discrete random

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This module introduces the Probability Distribution Function (PDF) and its characteristics.

A discrete probability distribution function has two characteristics:

• Each probability is between 0 and 1, inclusive.
• The sum of the probabilities is 1.

A child psychologist is interested in the number of times a newborn baby's crying wakes its mother after midnight. For a random sample of 50 mothers, the following information was obtained. Let $X$ = the number of times a newborn wakes its mother after midnight. For this example, $x$ = 0, 1, 2, 3, 4, 5.

$\text{P(x)}$ = probability that $X$ takes on a value $x$ .

 $x$ $\text{P(x)}$ 0 $\text{P(x=0)}=\frac{2}{50}$ 1 $\text{P(x=1)}=\frac{11}{50}$ 2 $\text{P(x=2)}=\frac{23}{50}$ 3 $\text{P(x=3)}=\frac{9}{50}$ 4 $\text{P(x=4)}=\frac{4}{50}$ 5 $\text{P(x=5)}=\frac{1}{50}$

$X$ takes on the values 0, 1, 2, 3, 4, 5. This is a discrete $\mathrm{PDF}$ because

1. Each $\text{P(x)}$ is between 0 and 1, inclusive.
2. The sum of the probabilities is 1, that is,

$\frac{2}{50}+\frac{11}{50}+\frac{23}{50}+\frac{9}{50}+\frac{4}{50}+\frac{1}{50}=1$

Suppose Nancy has classes 3 days a week. She attends classes 3 days a week 80% of the time, 2 days 15% of the time, 1 day 4% of the time, and no days 1% of the time. Suppose one week is randomly selected.

Let $X$ = the number of days Nancy ____________________ .

Let $X$ = the number of days Nancy attends class per week .

$X$ takes on what values?

0, 1, 2, and 3

Suppose one week is randomly chosen. Construct a probability distribution table (called a $\mathrm{PDF}$ table) like the one in the previous example. The table should have two columns labeled $x$ and $\text{P(x)}$ . What does the $\text{P(x)}$ column sum to?

 $x$ $\mathrm{P\left(x\right)}$ 0 0.01 1 0.04 2 0.15 3 0.80

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
how did you get the value of 2000N.What calculations are needed to arrive at it
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1 It is estimated that 30% of all drivers have some kind of medical aid in South Africa. What is the probability that in a sample of 10 drivers: 3.1.1 Exactly 4 will have a medical aid. (8) 3.1.2 At least 2 will have a medical aid. (8) 3.1.3 More than 9 will have a medical aid.