# 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

#### Questions & Answers

how can chip be made from sand
Eke Reply
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Almas
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Missy Reply
yeah
Joseph
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Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
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Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
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da
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Bhagvanji
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Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
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Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
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Professor
I think
Professor
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Alexandre
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Alexandre
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Brian Reply
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Rafiq
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Damian
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LITNING Reply
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LITNING Reply
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LITNING Reply
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LITNING
scanning tunneling microscope
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Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
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Rafiq
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Anam
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Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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Bob Reply
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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
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