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/sci/ - Science & Math

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11767086 No.11767086 [Reply] [Original]

why is the mean time not the same as the half-time in the exponential distribution?

how can I understand this intuitively ?

>> No.11767093
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11767093

>intuitively

>> No.11767097

>>11767093

every once in a while a retard like you comes along

>> No.11767131
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11767131

>>11767086
Infinite x makes mean larger than half-time.

>> No.11767320

>>11767131
What did you use to create that graph? tikz?

>> No.11767442

>>11767320
It's from wikipedia.
https://en.wikipedia.org/wiki/Exponential_distribution

>> No.11767774

>>11767086
Why would it be? It's a tailed distribution.

>> No.11768474

>>11767086
int_0^b (lambda e^(-lambda x)) dx = 1/2
int_0^(-lambda b) -e^u du = 1/2
1 - e^(-lambda b) = 1/2
e^(-lambda b) = 1/2
-lambda b = ln(1/2)
b = ln(1/2)/(-lambda) = ln(2)/lambda

while mean is 1/lambda