statistics

JIM Mil

Akron, OH, USA| Chicago, IL, USA

Apply
  • Experience

    Senior, Director
  • Education

    Masters , Phd/Doctorate
  • Industry

    Energy
  • Remote Option

    Yes remote
  • Job Perks

    N/A
  • Salary

    $140000
  • Location

    Akron, OH, USA| Chicago, IL, USA
  • Job Function

    other

Key Skills

Nuclear

Job Description Full Time

 

The simplest case of a normal distribution is known as the standard normal distribution. This is a special case when μ = 0 {\displaystyle \mu =0} \mu =0 and σ = 1 {\displaystyle \sigma =1} \sigma =1, and it is described by this probability density function:[1]

φ ( x ) = 1 2 π e − 1 2 x 2 {\displaystyle \varphi (x)={\frac {1}{\sqrt {2\pi }}}e^{-{\frac {1}{2}}x^{2}}} {\displaystyle \varphi (x)={\frac {1}{\sqrt {2\pi }}}e^{-{\frac {1}{2}}x^{2}}}

Here, the factor 1 / 2 π {\displaystyle 1/{\sqrt {2\pi }}} 1/{\sqrt {2\pi }} ensures that the total area under the curve φ ( x ) {\displaystyle \varphi (x)} \varphi (x) is equal to one.[note 1] The factor 1 / 2 {\displaystyle 1/2} 1/2 in the exponent ensures that the distribution has unit variance (i.e., variance being equal to one), and therefore also unit standard deviation. This function is symmetric around x = 0 {\displaystyle x=0} x=0, where it attains its maximum value 1 / 2 π {\displaystyle 1/{\sqrt {2\pi }}} 1/{\sqrt {2\pi }} and has inflection points at x = + 1 {\displaystyle x=+1} {\displaystyle x=+1} and x = − 1 {\displaystyle x=-1} x=-1.

Authors differ on which normal distribution should be called the "standard" one. Carl Friedrich Gauss, for example, defined the standard normal as having a variance of σ 2 = 1 / 2 {\displaystyle \sigma ^{2}=1/2} {\displaystyle \sigma ^{2}=1/2}. That is:

φ ( x ) = e − x 2 π {\displaystyle \varphi (x)={\frac {e^{-x^{2}}}{\sqrt {\pi }}}} {\displaystyle \varphi (x)={\frac {e^{-x^{2}}}{\sqrt {\pi }}}}

On the other hand, Stephen Stigler[7] goes even further, defining the standard normal as having a variance of σ 2 = 1 / ( 2 π ) {\displaystyle \sigma ^{2}=1/(2\pi )} {\displaystyle \sigma ^{2}=1/(2\pi )}:

φ ( x ) = e − π x 2 {\displaystyle \varphi (x)=e^{-\pi x^{2}}} {\displaystyle \varphi (x)=e^{-\pi x^{2}}}

General normal distribution

Every normal distribution is a version of the standard normal distribution, whose domain has been stretched by a factor σ {\displaystyle \sigma } \sigma (the standard deviation) and then translated by μ {\displaystyle \mu } \mu (the mean value):

f ( x ? μ , σ 2 ) = 1 σ φ ( x − μ σ ) {\displaystyle f(x\mid \mu ,\sigma ^{2})={\frac {1}{\sigma }}\varphi \left({\frac {x-\mu }{\sigma }}\right)} {\displaystyle f(x\mid \mu ,\sigma ^{2})={\frac {1}{\sigma }}\varphi \left({\frac {x-\mu }{\sigma }}\right)}

The probability density must be scaled by 1 / σ {\displaystyle 1/\sigma } 1/\sigma so that the integral is still 1.

If Z {\displaystyle Z} Z is a standard normal deviate, then X = σ Z + μ {\displaystyle X=\sigma Z+\mu } {\displaystyle X=\sigma Z+\mu } will have a normal distribution with expected value μ {\displaystyle \mu } \mu and standard deviation σ {\displaystyle \sigma } \sigma . Conversely, if X {\displaystyle X} X is a normal deviate with parameters μ {\displaystyle \mu } \mu and σ 2 {\displaystyle \sigma ^{2}} \sigma ^{2}, then the distribution Z = ( X − μ ) / σ {\displaystyle Z=(X-\mu )/\sigma } {\displaystyle Z=(X-\mu )/\sigma } will have a standard normal distribution. This variate is also called the standardized form of X {\displaystyle X} X.

Company Info.

JIM Mil

We are SDVI, a cutting-edge SaaS developer for Media & Entertainment, and we believe that the ideal company is a tight-knit team pursuing excellence and having fun along the way. We are a com
Project Management:
• Lead project scope development and options analysis and recommend technical solutions to meet customer needs (third party or in-house).
• Responsible for the creation of project plans, timelines, milestones, goals and ownership
• Must complete and implement projects on time, and ensure all assigned tasks and projects are executed to department quality standards.
• Plan, execute and report on the status of small to medium complex projects.
• Recognized as a technical lead for onshore and offshore teams on small and mid-sized projects.
• Other projects as assigned by the manager

Customer Experience:
• Work closely with mid to senior level management and project team during scope development and option analysis phase.
• Lead the technical aspects of the projects and/or solutions to meet client group expectations.
• Translate business requirements into technical/system requirements
• Execute technical solutions to department quality standards.

Analytics:
• Involved in research and analysis of third party software solutions, and must be able to make a recommendation to use third party software or develop solution in-house
• Identify future opportunities for application enhancement and value generation.
• Know how to break technical solutions into logical units, and have the ability to use models to show applications or program flow.

asdfasadfasdfasdfsadfa

asdfasdfasdfasdfsadfasdfsad

adsfasdfasdfasdfasdfasdfasdfasd

asdfasdfsadfsadfasdfasdfsadfa

Similar Jobs View More