Evaluate the Cumulative Distribution Function (CDF) at F(x,λ) = F(5,0.333333333)
CDF formula is below:
F(x,λ) = 1 - e-λxF(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
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 = √σ2σ = √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.
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
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
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