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LDR 5301-22.01.00-1B23-S1, Methods of Analysis for Business Operations•Unit IV Essay
Connie StanleyTotal Score:highRisk Created with Sketch.
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NORMAL, POISSON, AND EXPONENTIAL DISTRIBUTIONS 2 Normal, Poisson, and Exponential Distributions
Connie Stanley
1Columbia Southern University
September 3, 2022
1The differences between Poisson, Normal, and Exponential Distributions
2Continuous random variables and discrete random variables are the two types of random variables.
As a result, there are two kinds of continuous distributions:
3probability distributions and discrete probability distributions.
4The exponential and normal distributions are continuous distributions, whereas the Poisson distribution is discontinuous.
Any statistician must understand their definition, qualities, and application in real-world circumstances.
5As a result, this essay analyzes the significant differences between the normal, exponential, and Poisson distributions.
1Furthermore, it provides a full explanation of the exponential distribution while discussing the conditions in which it is useful for data analysis and one real-world application.
Equivalent distribution
1The time between events in a toxic process is represented by the exponential distribution, a kind of continuous probability distribution (Australian Mathematical Sciences Institute (AMSI), 2020).
3In essence, it denotes the amount of time that must pass following one occurrence before the next can take place.
Its mathematical formula is:
1f(x) = ex Where e is the base of natural logarithms and equals 2.718, x is the random variable, is the average number of units, and is the average number of units.
6The following formula represents the probability distribution function (pdf) of x:
3fx(x) = {µe−µxif x>0 0otherwise
The exponential distribution is crucial for predicting radioactive decay, detecting the spread of a novel disease like COVID-19 among a broader population, and evaluating internet packet data.
They deal with information that occurs over time periods such a day, a day, a month, a term, and a year.
6For instance, we may utilize exponential distribution to examine how many births take place in a particular hospital across the nation.
If we assume that X is the space in time between hospital births, with a 30-day median, then.
1Once more under the presumption that the distribution of births is exponential, every birth is treated as a single birth regardless of whether it is triplets or twins. In this situation, a single day with an aggregate becomes the unit of time of birth after every 30 days as µ =.
Thus X d = exp( ) and fx(x) = 301 e−301 xif x>0{
else
The outcomes are as follows when using the exponential distribution's mean and variance properties:
1αx = E(X) = 30 days (for mean) σ2x = var(X) = 900 σx = sd(X) = 30 days
Using the preceding results, the following basic formula can be used to calculate the likelihood of giving birth within the next 15 days:
7−1 x for x ?0
1Fx(x) = 1- e 30 As a result, the likelihood that the waiting period for the next birth will be fifteen days in the following fifteen days is provided by: Fx(15) = 1 - e for x ?0 = 1 - e−0.5 = 0.39346
The below graph of f(x) versus x will be used to show the example:x
Because the process does not retain memories of previous events, the exponential distribution has the characteristic of lacking memory, and the helping time distribution surpasses that length of time at x = 0.
1It produces a result of zero when the random variable x is negative or less than zero.
The aforementioned findings can be used in my company to investigate the rate of sales since they can be used to examine daily sales patterns.
1The time between sales, which is typically 12 hours, can represent the random variable T. In calculating the chances of making the following sale in the next hour, 2 hours, or ten hours, it will adhere to the example given. The Significant Differences The normality test is a continuous symmetric probability distribution with a central limit theorem. According to the Australian Mathematical Sciences Institute (2020), if X has a Normally distributed with mean and standard deviation, we write X d = N(, 2); the probability density function of X is provided by: fx(x) = for x ∈ ℝ.
3In contrast to the Poisson and exponential distributions, the normal probability features a bell curve with a symmetric probability distribution that has one peak at the position x =.
1The Poisson distribution only considers occurrences with a set duration (Zhao et al., 2020). The time between events in a toxic process, however, is represented by the exponential distribution.
4Once more, the exponential and normal distributions are continuous, whereas the Poisson distribution is discontinuous.
3The Poisson and exponential distributions each have one pdf, whereas the normal distribution contains two pdfs with two inflection points of distinct signs: x = and x = +.
References
3Australian Mathematical Sciences Institute (AMSI), (2020).
8Probability and Statistics:
1Module 22 on Exponential and Normal Distributions. Zhao, J., Zhang, F., Zhao, C., Wu, G., Wang, H., & Cao, X.
(2020, May).
1The Properties and Application of Poisson Distribution. In Journal of Physics:
Conference Series This study source was downloaded by 100000848136341 from CourseHero.com on 08-31-2022 15:05:18 GMT -05:00
https://www.coursehero.com/file/84832081/Unit-IV-Essay-MSL-5080docx/
Source Matches (29)- 1Student paper94%
Student paper
NORMAL, POISSON, AND EXPONENTIAL DISTRIBUTIONS 2 Normal, Poisson, and Exponential Distributions
Original source
Normal, Poisson, and Exponential Distributions Normal, Poisson, and Exponential Distributions
- 1Student paper100%
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Columbia Southern University
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Columbia Southern University
- 1Student paper83%
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The differences between Poisson, Normal, and Exponential Distributions
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Normal, Poisson, and Exponential Distributions
- 2Student paper76%
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Continuous random variables and discrete random variables are the two types of random variables.
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Continuous random variables are classified two different ways, either continuous random variables or discrete random variables
- 3Student paper89%
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probability distributions and discrete probability distributions.
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That creates probability distributions and discrete probability distributions
- 4Student paper74%
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The exponential and normal distributions are continuous distributions, whereas the Poisson distribution is discontinuous.
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Normal and exponential are both continuous distributions whereas Poisson distribution is discrete and always changing
- 5Student paper68%
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As a result, this essay analyzes the significant differences between the normal, exponential, and Poisson distributions.
Original source
In this this essay, I will discuss the major differences between normal, exponential, and Poisson distributions
- 1Student paper71%
Student paper
Furthermore, it provides a full explanation of the exponential distribution while discussing the conditions in which it is useful for data analysis and one real-world application.
Original source
Besides, it provides a detailed explanation of exponential distribution while describing the situations in which it is useful for analyzing data and one real-world example of its application
- 1Student paper84%
Student paper
The time between events in a toxic process is represented by the exponential distribution, a kind of continuous probability distribution (Australian Mathematical Sciences Institute (AMSI), 2020).
Original source
The exponential distribution is a type of continuous probability distribution that represents the time between events in a poison process (Australian Mathematical Sciences Institute (AMSI), 2020)
- 3Student paper63%
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In essence, it denotes the amount of time that must pass following one occurrence before the next can take place.
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For one thing, it stands for the amount of time that must pass before something else can take place
- 1Student paper85%
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f(x) = ex Where e is the base of natural logarithms and equals 2.718, x is the random variable, is the average number of units, and is the average number of units.
Original source
f(x) = µ Where x is the random variable, µ is the average number of units, and e is the base of natural logarithms and it equals to 2.718
- 6Student paper71%
Student paper
The following formula represents the probability distribution function (pdf) of x:
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Thus the probability distribution function (pdf) of x is
- 3Student paper64%
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fx(x) = {µe−µxif x>0 0otherwise
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fx (x) = { 1 e 1 x if x>0 30 30 0otherwise
- 6Student paper67%
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For instance, we may utilize exponential distribution to examine how many births take place in a particular hospital across the nation.
Original source
For instance, we can utilize exponential distribution to study the amount of births that take place in a hospital in our country
- 1Student paper73%
Student paper
Once more under the presumption that the distribution of births is exponential, every birth is treated as a single birth regardless of whether it is triplets or twins. In this situation, a single day with an aggregate becomes the unit of time of birth after every 30 days as µ =.
Original source
Again, with the assumption that the distribution between the births is exponential and does not consider birth of triplets or twins but treats every birth as a single birth In this case, the unit time becomes a day with an average of birth after every 30 days as µ =
- 1Student paper81%
Student paper
αx = E(X) = 30 days (for mean) σ2x = var(X) = 900 σx = sd(X) = 30 days
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αx = E(X) = 30 days (for mean) σ2x = var(X) = 900
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−1 x for x ?0
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x 1 0
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Fx(x) = 1- e 30 As a result, the likelihood that the waiting period for the next birth will be fifteen days in the following fifteen days is provided by: Fx(15) = 1 - e for x ?0 = 1 - e−0.5 = 0.39346
Original source
Fx(x) = 1- for x Therefore in the next fifteen days the probability that with waiting time for the next birth will be fifteen days is given by Fx(15) = 1 - for x = 1 - = 0.39346
- 1Student paper84%
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It produces a result of zero when the random variable x is negative or less than zero.
Original source
Where the random variable x is negative or less than zero, it returns a zero result
- 1Student paper71%
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The time between sales, which is typically 12 hours, can represent the random variable T. In calculating the chances of making the following sale in the next hour, 2 hours, or ten hours, it will adhere to the example given. The Significant Differences The normality test is a continuous symmetric probability distribution with a central limit theorem. According to the Australian Mathematical Sciences Institute (2020), if X has a Normally distributed with mean and standard deviation, we write X d = N(, 2);
Original source
The random variable T can be the interval between sales, and the average time for sales is 12 hours It will follow the example provided in determining the probability of making the next sale within an hour, two hours, or ten hours The normal distribution is symmetric continuous probability distribution of a central limit theorem Australian Mathematical Sciences Institute (2020) defines that If X has a Normal distribution with mean µ and standard deviation σ, then we write that X d = N(µ,σ 2 )
- 1Student paper92%
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the probability density function of X is provided by: fx(x) = for x ∈ ℝ.
Original source
the probability density function of X is given by fx(x) = for x ∈ ℝ
- 3Student paper82%
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In contrast to the Poisson and exponential distributions, the normal probability features a bell curve with a symmetric probability distribution that has one peak at the position x =.
Original source
Unlike Poisson and exponential distributions, normal probability has a symmetric bell curve with one peak at x =
- 1Student paper68%
Student paper
The Poisson distribution only considers occurrences with a set duration (Zhao et al., 2020). The time between events in a toxic process, however, is represented by the exponential distribution.
Original source
Poisson distribution only deals with events that have a fixed period of time (Zhao et al., 2020) However, the exponential distribution represents the time between events in a poison process
- 4Student paper73%
Student paper
Once more, the exponential and normal distributions are continuous, whereas the Poisson distribution is discontinuous.
Original source
Normal and exponential are both continuous distributions whereas Poisson distribution is discrete and always changing
- 3Student paper82%
Student paper
The Poisson and exponential distributions each have one pdf, whereas the normal distribution contains two pdfs with two inflection points of distinct signs: x = and x = +.
Original source
Normal distribution pdf contains two inflection points with different signs x = and x = +
- 3Student paper100%
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Australian Mathematical Sciences Institute (AMSI), (2020).
Original source
Australian Mathematical Sciences Institute (AMSI), (2020)
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Probability and Statistics:
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Probability and statistics
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Module 22 on Exponential and Normal Distributions. Zhao, J., Zhang, F., Zhao, C., Wu, G., Wang, H., & Cao, X.
Original source
Module 22 on Exponential and Normal Distributions Zhao, J., Zhang, F., Zhao, C., Wu, G., Wang, H., & Cao, X
- 1Student paper100%
Student paper
The Properties and Application of Poisson Distribution. In Journal of Physics:
Original source
The Properties and Application of Poisson Distribution In Journal of Physics
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