Evaluate the CDF at (x,) = ( 5,0.333333333)
Publish date: 2024-05-13
Evaluate the CDF at ƒ(x,λ) = ƒ( 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
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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
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This calculator has 2 inputs.
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ƒ(x,λ) = λe-λxF(x,λ) = 1 - e-λx
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