Manuals/calci/EXPONDIST

EXPONDIST(x,Lambda,cum)

• $x$ is the value of the function
• $lambda$ 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 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), xis 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

Failed to parse (syntax error): {\displaystyle f(x;\lambda)= λe^{-\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 : $F(x;\lambda )=1-e^{-\lambda x},x\geq 0$

$0,x<0$

or

$F(x,\lambda )=1-e^{-\lambda x}.H(x)$

• 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}{ λ}}
• The variance of the Exponential Distribution is: $Var[x]={\frac {1}{\lambda ^{2}}}$.

Examples

Question : If jobs arrive at an average of 15 seconds, λ = 5 per minute, what is the probability of waiting 30 seconds, i.e 0.5 min? Here λ=5 and x=0.5 =EXPONDIST(0.5,5,TRUE)=0.917915001 =EXPONDIST(5,3,TRUE)=0.999999694 =EXPONDIST(0.4,2,FALSE)=0.898657928"