Manuals/calci/EXPONDIST

EXPONDIST(x,lambda,cu)

• $x$ is the value of the function
• $lambda(\lambda )$ is the value of the rate parameter
• $cu$ is the logical value like TRUE or FALSE

Description

• This function gives the Exponential Distribution. This distribution is used to model the time until something happens in the process.
• This describes the time between events in a Poisson process i.e, a process in which events occur continuously and independently at a constant average rate.
• For e.g Time between successive vehicles arrivals at a workshop.
• In $EXPONDIST(x,lambda,cu)$, $x$ is the value of the function, $lambda$ is called rate parameter and $cu$(cumulative) is the TRUE or FALSE.
• This function will give the Cumulative Distribution Function when $cu$ is TRUE, otherwise it will give the Probability Density Function , when $cu$ is FALSE.
• Suppose we are not giving the $cu$ value, by default it will consider the $cu$ value is FALSE.
• This function will give the error result when

1. $x$ or $\lambda$ is non-numeric.
2. $x<0$ or $lambda\leq 0$

The Probability Density Function of an Exponential Distribution is

$f(x,\lambda )=\lambda e^{-\lambda x},x\geq 0$

$=0,x<0$

or

$f(x;\lambda )=\lambda e^{-\lambda x}.H(x)$

• where $\lambda$ is the rate parameter and $H(x)$ is the Heaviside step function
• This function is valid only on the interval [0,infinity].

The Cumulative Distribution Function is : Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F(x;\lambda)=1-e^{-\lambda x}, x \ge 0}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0 , x<0 }

or

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F(x,\lambda)=1-e^{-\lambda x}.H(x)}

• The mean or expected value of the Exponential Distribution is: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E[x]=\frac{1}{\lambda}}
• The variance of the Exponential Distribution is: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Var[x]=\frac{1}{\lambda^2}} .

Examples

Question : If jobs arrive at an average of 15 seconds, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lambda =5} per minute, what is the probability of waiting 30 seconds, i.e 0.5 min? Here Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lambda =5} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x=0.5}

• =EXPONDIST(0.5,5,TRUE) = 0.917915001
• =EXPONDIST(5,3,TRUE) = 0.999999694
• =EXPONDIST(0.4,2,FALSE) = 0.898657928"

See Also

• GAMMADIST
• POISSONDISTRIBUTION

References

• Exponential Distribution