# 5.4 Summary of the uniform and exponential probability distributions

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This module provides a summary of formulas and definitions related to Continuous Random Variables.
Formula

## Uniform

$X$ = a real number between $a$ and $b$ (in some instances, $X$ can take on the values $a$ and $b$ ). $a$ = smallest $X$ ; $b$ = largest $X$

$X$ ~ $U\left(\mathrm{a,}b\right)$

The mean is $(\mu , \frac{a+b}{2})$

The standard deviation is $(\sigma , \sqrt{\frac{\left(b-a{\right)}^{2}}{12}})$

Probability density function: $f(X)=\frac{1}{b-a}$ for $((a, X), b)$

Area to the Left of x: $((P\left(X, x\right)), \text{(base)}\text{(height)})$

Area to the Right of x: $((P\left(X, x\right)), \text{(base)}\text{(height)})$

Area Between c and d: $((((P\left(c, X), d\right)), \left(\text{base}\right)\left(\text{height}\right)), \left(d-c\right)\left(\text{height}\right))$ .

Formula

## Exponential

$X$ ~ $\mathrm{Exp}\left(m\right)$

$X$ = a real number, 0 or larger. $m$ = the parameter that controls the rate of decay or decline

The mean and standard deviation are the same.

$\mu =\sigma =\frac{1}{m}$ and $m=\frac{1}{\mu }=\frac{1}{\sigma }$

The probability density function: $f\left(X\right)=m\cdot {e}^{\mathrm{-m\cdot X}}$ , $(X, 0)$

Area to the Left of x: $((P\left(X, x\right)), 1-{e}^{\mathrm{-m\cdot x}})$

Area to the Right of x: $((P\left(X, x\right)), {e}^{\mathrm{-m\cdot x}})$

Area Between c and d: $((P\left(c, X), d\right))=(P\left(X, d\right))-(P\left(X, c\right))=\left(1-{e}^{\mathrm{- m\cdot d}}\right)-\left(1-{e}^{\mathrm{- m\cdot c}}\right)={e}^{\mathrm{- m\cdot c}}-{e}^{\mathrm{- m\cdot d}}$

Percentile, k: $k=\frac{\text{LN(1-AreaToTheLeft)}}{\mathrm{-m}}$

what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
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Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
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LITNING
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Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
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?
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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 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. By     By   By 