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Here's an logarithmic fact that I've made use of frequently: If X is a random variable having a uniform distribution between zero and one, then –ln( X )/ λ has an exponential distribution with rate λ . This relationship comes in handy when, for example, you want to draw weighted random samples. Or generating event times for simulations.
How long do I have to study math to understand this?
Here's an logarithmic fact that I've made use of frequently: If X is a random variable having a uniform distribution between zero and one, then –ln( X )/ λ has an exponential distribution with rate λ . This relationship comes in handy when, for example, you want to draw weighted random samples. Or generating event times for simulations.
How long do I have to study math to understand this?
Earlier quoted context omitted.
https://mathcenter.oxford.emory.edu/site/math108/logs/ Some people have suggested the "triangle of power".
The Triangle of power explanation of logarithms is what really got me across logs. It wasn't until seeing the triangle and having the relationships explained that I had any clue about logarithms, up until then logs had been some archaic number that meant nothing to me. Because of the triangle of power, I now rock up to B and B+ Trees and calculate the number of disc accesses each will require in the worst case, depen…
But my absolute favorite trick is base conversions, https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:... with some practice you can do approximate base conversions (power to 2 to power of 10 or e) in your head
Here's an logarithmic fact that I've made use of frequently: If X is a random variable having a uniform distribution between zero and one, then –ln( X )/ λ has an exponential distribution with rate λ . This relationship comes in handy when, for example, you want to draw weighted random samples. Or generating event times for simulations.
How long do I have to study math to understand this?
If Y=-ln(X)/lambda, then P(Yexp(-lambda a)) = 1-exp(-lambda a).
And if Z is exponential with rate parameter lambda, then P(ZThey have the same PDF, so they're the same distribution.
(I'm sure this is in the book) John Napier, the father of logarithms (the N in ln), basically had a sweatshop of human calculators making log tables over something like 20 years - critical for celestial navigation. There was a huge price attached to the person that developed a method to safely navigate across the oceans, also lead to the invention of the pocket watch
Here's an logarithmic fact that I've made use of frequently: If X is a random variable having a uniform distribution between zero and one, then –ln( X )/ λ has an exponential distribution with rate λ . This relationship comes in handy when, for example, you want to draw weighted random samples. Or generating event times for simulations.
How long do I have to study math to understand this?
Earlier quoted context omitted.
How long do I have to study math to understand this?
I love that you asked this, but I think it's not quite the right question. I've been wishing for years that someone would maintain a "dependency graph" for mathematical concepts. I think Khan Academy tried to do something like this at one point but took it down a long time ago. As long as we're far enough from the bleeding-edge of research topics, I feel like maths is the one field where this might be possible to do…