The document discusses the normal distribution and its key characteristics. It defines the normal distribution as a bell-shaped curve that is symmetric around the mean. The normal distribution is determined by its mean and standard deviation. Some common applications of the normal distribution include measuring heights, weights, IQ scores, and test results. The standard normal distribution has a mean of 0 and standard deviation of 1. Z-scores indicate how many standard deviations above or below the mean a data point lies.
Normal Distribution – Introduction and PropertiesSundar B N
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Normal Distribution – Introduction and PropertiesSundar B N
In this video you can see Normal Distribution – Introduction and Properties.
Watch the video on above ppt
https://www.youtube.com/watch?v=ocTXHLWsec8&list=PLBWPV_4DjPFO6RjpbyYXSaZHiakMaeM9D&index=4
Subscribe to Vision Academy
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The Normal Distribution is a symmetrical probability distribution where most results are located in the middle and few are spread on both sides. It has the shape of a bell and can entirely be described by its mean and standard deviation.
Turning from discrete to continuous distributions, in this section we discuss the normal distribution. This is the most important continuous distribution because in applications many random variables are normal random variables (that is, they have a normal distribution) or they are approximately normal or can be transformed into normal random variables in a relatively simple fashion. Furthermore, the normal distribution is a useful approximation of more complicated distributions, and it also occurs in the proofs of various statistical tests.
Normal Distribution, also called Gaussian Distribution, is one of the widely used continuous distributions existing which is used to model a number of scenarios such as marks of students, heights of people, salaries of working people etc.
Each binomial distribution is defined by n, the number of trials and p, the probability of success in any one trial.
Each Poisson distribution is defined by its mean.
In the same way, each Normal distribution is identified by two defining characteristics or parameters: its mean and standard deviation.
The Normal distribution has three distinguishing features:
• It is unimodal, in other words there is a single peak.
• It is symmetrical, one side is the mirror image of the other.
• It is asymptotic, that is, it tails off very gradually on each side but the line representing the distribution never quite meets the horizontal axis
The Normal Distribution is a symmetrical probability distribution where most results are located in the middle and few are spread on both sides. It has the shape of a bell and can entirely be described by its mean and standard deviation.
Turning from discrete to continuous distributions, in this section we discuss the normal distribution. This is the most important continuous distribution because in applications many random variables are normal random variables (that is, they have a normal distribution) or they are approximately normal or can be transformed into normal random variables in a relatively simple fashion. Furthermore, the normal distribution is a useful approximation of more complicated distributions, and it also occurs in the proofs of various statistical tests.
Normal Distribution, also called Gaussian Distribution, is one of the widely used continuous distributions existing which is used to model a number of scenarios such as marks of students, heights of people, salaries of working people etc.
Each binomial distribution is defined by n, the number of trials and p, the probability of success in any one trial.
Each Poisson distribution is defined by its mean.
In the same way, each Normal distribution is identified by two defining characteristics or parameters: its mean and standard deviation.
The Normal distribution has three distinguishing features:
• It is unimodal, in other words there is a single peak.
• It is symmetrical, one side is the mirror image of the other.
• It is asymptotic, that is, it tails off very gradually on each side but the line representing the distribution never quite meets the horizontal axis
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Chapter 6: Normal Probability Distribution
6.1: The Standard Normal Distribution
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Nutraceutical market, scope and growth: Herbal drug technologyLokesh Patil
As consumer awareness of health and wellness rises, the nutraceutical market—which includes goods like functional meals, drinks, and dietary supplements that provide health advantages beyond basic nutrition—is growing significantly. As healthcare expenses rise, the population ages, and people want natural and preventative health solutions more and more, this industry is increasing quickly. Further driving market expansion are product formulation innovations and the use of cutting-edge technology for customized nutrition. With its worldwide reach, the nutraceutical industry is expected to keep growing and provide significant chances for research and investment in a number of categories, including vitamins, minerals, probiotics, and herbal supplements.
Introduction:
RNA interference (RNAi) or Post-Transcriptional Gene Silencing (PTGS) is an important biological process for modulating eukaryotic gene expression.
It is highly conserved process of posttranscriptional gene silencing by which double stranded RNA (dsRNA) causes sequence-specific degradation of mRNA sequences.
dsRNA-induced gene silencing (RNAi) is reported in a wide range of eukaryotes ranging from worms, insects, mammals and plants.
This process mediates resistance to both endogenous parasitic and exogenous pathogenic nucleic acids, and regulates the expression of protein-coding genes.
What are small ncRNAs?
micro RNA (miRNA)
short interfering RNA (siRNA)
Properties of small non-coding RNA:
Involved in silencing mRNA transcripts.
Called “small” because they are usually only about 21-24 nucleotides long.
Synthesized by first cutting up longer precursor sequences (like the 61nt one that Lee discovered).
Silence an mRNA by base pairing with some sequence on the mRNA.
Discovery of siRNA?
The first small RNA:
In 1993 Rosalind Lee (Victor Ambros lab) was studying a non- coding gene in C. elegans, lin-4, that was involved in silencing of another gene, lin-14, at the appropriate time in the
development of the worm C. elegans.
Two small transcripts of lin-4 (22nt and 61nt) were found to be complementary to a sequence in the 3' UTR of lin-14.
Because lin-4 encoded no protein, she deduced that it must be these transcripts that are causing the silencing by RNA-RNA interactions.
Types of RNAi ( non coding RNA)
MiRNA
Length (23-25 nt)
Trans acting
Binds with target MRNA in mismatch
Translation inhibition
Si RNA
Length 21 nt.
Cis acting
Bind with target Mrna in perfect complementary sequence
Piwi-RNA
Length ; 25 to 36 nt.
Expressed in Germ Cells
Regulates trnasposomes activity
MECHANISM OF RNAI:
First the double-stranded RNA teams up with a protein complex named Dicer, which cuts the long RNA into short pieces.
Then another protein complex called RISC (RNA-induced silencing complex) discards one of the two RNA strands.
The RISC-docked, single-stranded RNA then pairs with the homologous mRNA and destroys it.
THE RISC COMPLEX:
RISC is large(>500kD) RNA multi- protein Binding complex which triggers MRNA degradation in response to MRNA
Unwinding of double stranded Si RNA by ATP independent Helicase
Active component of RISC is Ago proteins( ENDONUCLEASE) which cleave target MRNA.
DICER: endonuclease (RNase Family III)
Argonaute: Central Component of the RNA-Induced Silencing Complex (RISC)
One strand of the dsRNA produced by Dicer is retained in the RISC complex in association with Argonaute
ARGONAUTE PROTEIN :
1.PAZ(PIWI/Argonaute/ Zwille)- Recognition of target MRNA
2.PIWI (p-element induced wimpy Testis)- breaks Phosphodiester bond of mRNA.)RNAse H activity.
MiRNA:
The Double-stranded RNAs are naturally produced in eukaryotic cells during development, and they have a key role in regulating gene expression .
Multi-source connectivity as the driver of solar wind variability in the heli...Sérgio Sacani
The ambient solar wind that flls the heliosphere originates from multiple
sources in the solar corona and is highly structured. It is often described
as high-speed, relatively homogeneous, plasma streams from coronal
holes and slow-speed, highly variable, streams whose source regions are
under debate. A key goal of ESA/NASA’s Solar Orbiter mission is to identify
solar wind sources and understand what drives the complexity seen in the
heliosphere. By combining magnetic feld modelling and spectroscopic
techniques with high-resolution observations and measurements, we show
that the solar wind variability detected in situ by Solar Orbiter in March
2022 is driven by spatio-temporal changes in the magnetic connectivity to
multiple sources in the solar atmosphere. The magnetic feld footpoints
connected to the spacecraft moved from the boundaries of a coronal hole
to one active region (12961) and then across to another region (12957). This
is refected in the in situ measurements, which show the transition from fast
to highly Alfvénic then to slow solar wind that is disrupted by the arrival of
a coronal mass ejection. Our results describe solar wind variability at 0.5 au
but are applicable to near-Earth observatories.
Richard's aventures in two entangled wonderlandsRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...Sérgio Sacani
Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
on Io’s surface have been monitored from both spacecraft and ground-based telescopes.
Here, we present the highest spatial resolution images of Io ever obtained from a groundbased telescope. These images, acquired by the SHARK-VIS instrument on the Large
Binocular Telescope, show evidence of a major resurfacing event on Io’s trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images
show that a plume deposit from a powerful eruption at Pillan Patera has covered part
of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io’s surface using adaptive
optics at visible wavelengths.
1. TOPIC : Normal Distribution
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Made by : Noor-ul-ain
2. Normal distribution
Normal curve
Characteristics
Normal random variable
Standard normal distribution
Standard scores
Applications
3.
4. Definition:
Normal distribution, also known as the Gaussian
distribution, is a probability distribution that is symmetric about
the mean, showing that data near the mean or more frequent in
occurrence than data from the mean.
In graph form, normal distribution will appear as bell curve.
History:
In 1733, DeMoivre derived the mathematical equation of
normal curve. It is often referring to as the Gaussian Distribution in
honor of Gauss (1777-1855), who also derived its equation from a
study of errors in repeated measurements of the same quantity.
5. Definition:
A normal curve is a bell-shaped curve which shows
the probability distribution of a continuous random variable.
Moreover, the normal curve represents a normal distribution.
The total area under the normal curve logically represents the
sum of all probabilities for a random variables. Hence, the area
under the normal curve is one. Also, the standard normal curve
represents a normal curve with mean 0 and standard deviation 1.
Thus, the parameters involved in a normal distributions is mean (µ)
and standard deviation (Ϭ).
6.
7. Characteristics of a Normal Curve:
The values of mean, median and mode are same
It represents a unimodal distribution as it has only one peak.
It shows a symmetric distribution as 50% of the data set lies
on the left side of the mean and 50% of the data set lies on
the right side of the mean.
Empirical rule: 68% of the data fall within µ ± б , 95% of the
data fall within µ ± 2б and 99.7% of the data fall within µ ±
3б.
8. Some examples for normal distribution are given below:
• Heights/weights of the subjects under study
• IQ scores of the students
• Test scores of the students
9. A continuous random variable X having the bell-shaped
distribution as shown in the fig, is called a normal random
variable. The mathematical equation for the probability
distribution of the normal variable depends upon the two
parameters µ and б, its mean and standard deviation. Hence, we
denote the values of the density function of X by n(x; µ, б).
10. Definition :
The distribution of a normal random
variable with mean zero and standard
deviation equal to one is a standard normal
distribution .
11.
12. Definition :
The value on the standard normal
distribution is known as a standard score or a
Z-score .
A standard score represents a number
of standard deviations above or below the
mean that a specific observation falls .
13. Z-score is equal to ,
z = x-µ
б
where x is the random variable and µ is the mean and б is the
standard deviation .
14. A radar unit is used to measure speed of cars on the motorway .
The speed are normally distributed with a mean of 90 km/hr
and standard deviation 10 km/hr . What is the probability
that a car picked at random is travelling at more than 100km
/hr ?
answer :
Let X be the random sample, so X has µ=90 , б=10
Then we must find P(x>100)
For x=100 , so z=1
For P(x>90)=P(Z>1)= total area –area to the left z=1
=1-0.8413 = 0.1587
The probability P(X>100) is equal to 0.1587
15. (1) The main reason that the normal distribution is so
popular is because it works . The reason that it works is
really because of the central limit theorem .
(2) A standard normal distribution can often be used to
solve practical application problems like IQ level of
students .
(3) In order to use it , the variables must be normally (or
approximately normally) distributed (bell shaped
graph).
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