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

Evaluate the CDF at ƒ(x,λ) = ƒ( 5,0.333333333) 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?

density: The compactness measure of an object
distribution: value range for a variable
entropy: refers to disorder or uncertainty
exponential: of or relating to an exponent
exponential distribution: probability distribution that describes the time between events in a Poisson point process
mean: A statistical measurement also known as the average
standard deviation: a measure of the amount of variation or dispersion of a set of values. The square root of variance
variance: How far a set of random numbers are spead out from the mean