Evaluate the CDF at (x,) = ( 5,0.333333333)

Publish date: 2024-05-13
Evaluate the CDF at ƒ(x,λ) = ƒ( 5,0.333333333) MathCelebrity logo Image to Crop Evaluate the Cumulative Distribution Function (CDF) at F(x,λ) = F(5,0.333333333)

CDF formula is below:

F(x,λ) = 1 - e-λx
F(5,0.333333333) = 1 - 2.718281828459(-0.333333333)(5)
F(5,0.333333333) = 1 - 2.718281828459-1.666666665
F(5,0.333333333) = 1 - 0.18887560315235

F(5,0.333333333) = 0.81112439684765

You have 1 free calculations remaining


Calculate the mean (μ):

μ  =  1
  λ

μ  =  1
  0.333333333

μ = 3.000000003

Calculate the median:

Median  =  Ln(2)
  λ

Median  =  0.69314718055995
  0.333333333

Median = 2.0794415437593

Calculate the variance (σ2):

σ2  =  1
  λ2

σ2  =  1
  0.3333333332

σ2  =  1
  0.11111111088889

σ2 = 9.000000018

Calculate Standard Deviation which is the square root of variance denoted as σ

σ = √σ2
σ = √9.000000018
σ = 3.000000003

Calculate entropy:

Entropy = 1 - Ln(λ)
Entropy = 1 - Ln(0.333333333)
Entropy = 1 - -1.0986122896681
Entropy = 2.0986122896681

What is the Answer?

F(5,0.333333333) = 0.81112439684765

How does the Exponential Distribution Calculator work?

Free Exponential Distribution Calculator - Calculates the Probability Density Function (PDF) and Cumulative Density Function (CDF) of the exponential distribution as well as the mean, variance, standard deviation, and entropy.
This calculator has 2 inputs.

What 6 formulas are used for the Exponential Distribution Calculator?

ƒ(x,λ) = λe-λx
F(x,λ) = 1 - e-λx
μ = 1/λ
Median = Ln(2)/λ
σ2 = 1/λ2
Entropy = 1 -Ln(λ)

For more math formulas, check out our Formula Dossier

What 8 concepts are covered in the Exponential Distribution Calculator?

densityThe compactness measure of an objectdistributionvalue range for a variableentropyrefers to disorder or uncertaintyexponentialof or relating to an exponentexponential distributionprobability distribution that describes the time between events in a Poisson point processmeanA statistical measurement also known as the averagestandard deviationa measure of the amount of variation or dispersion of a set of values. The square root of variancevarianceHow far a set of random numbers are spead out from the mean

Exponential Distribution Calculator Video


Tags:

Add This Calculator To Your Website

ncG1vNJzZmivp6x7rq3ToZqepJWXv6rA2GeaqKVfmsWxu8Oiqq1moJ29gMScZGxfpG1le3R%2FkmxqbGtjaHOxuJx8e38%3D