Probability Distribution Quotes

If you hear a "prominent" economist using the word 'equilibrium,' or 'normal distribution,' do not argue with him; just ignore him, or try to put a rat down his shirt.

There is no such thing as luck; there is only adequate or inadequate preparation to cope with a statistical universe.

This branch of mathematics [Probability] is the only one, I believe, in which good writers frequently get results which are entirely erroneous.

Although we deal with probabilities and expectations, the actual results can deviate substantially from such expectations, particularly on a short-term basis.

If there's no limit to how big the entropy can get, then you can start anywhere, and from that starting point, you'd expect entropy to rise as the system moves to explore larger and larger regions of phase space.

I'm always trying to calculate the mathematical probability of certain outcomes.

Maybe we should teach schoolchildren probability theory and investment risk management.

One of the laws of nature," Gordon said, "is that half the people have got to be below average.""For a Gaussian distribution, yeah," Cooper said. "Sad, though.

In no other branch of mathematics is it so easy for experts to blunder as in probability theory.

Random chance is not sufficient to explain random chance. ~Jubal Harshaw

Skill is a function of chance. It’s an intuitive best-use of chance situations.

We know the laws of trial and error, of large numbers and probabilities. We know that these laws are part of the mathematical and mechanical fabric of the universe, and that they are also at play in biological processes. But, in the name of the experimental method and out of our poor knowledge, are we really entitled to claim that everything happens by chance, to the exclusion of all other possibilities?

Maximum of an average is necessarily less volatile than the average maximum.

Fourth Law of Thermodynamics: If the probability of success is not almost one, then it is damn near zero.

I am fully assured, that no general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognize, not only the special numerical bases of the science, but also those universal laws of thought which are the basis of all reasoning, and which, whatever they may be as to their essence, are at least mathematical as to their form.

We must become more comfortable with probability and uncertainty.

I failed math twice, never fully grasping probability theory. I mean, first off, who cares if you pick a black ball or a white ball out of the bag? And second, if you’re bent over about the color, don’t leave it to chance. Look in the damn bag and pick the color you want.

A 99% Value-at-Risk calculation does not evaluate what happens in the last one percent... This is like an airbag that works all the time, except when you have a car accident.

My favourite fellow of the Royal Society is the Reverend Thomas Bayes, an obscure 18th-century Kent clergyman and a brilliant mathematician who devised a complex equation known as the Bayes theorem, which can be used to work out probability distributions. It had no practical application in his lifetime, but today, thanks to computers, is routinely used in the modelling of climate change, astrophysics and stock-market analysis.

In mathematics, as in physics, so much depends on chance, on a propitious moment.

[On the Gaussian curve, remarked to Poincaré:] Experimentalists think that it is a mathematical theorem while the mathematicians believe it to be an experimental fact.

Averages are useful because many traits, behaviors, and outcomes are distributed in a bell-shaped curve, with most results clustered around the middle and a much smaller group of outliers at the high and low ends.

I've debated many economists who claim to specialize in risk and probability: when one takes them slightly outside their narrow focus, but within the discipline of probability, they fall apart, with the disconsolate face of a gym rat in front of a gangster hit man.

In physics the truth is rarely perfectly clear, and that is certainly universally the case in human affairs. Hence, what is not surrounded by uncertainty cannot be the truth.

But it is necessary to insist more strongly than usual that what I am putting before you is a model-the Bohr model atom-because later I shall take you to a profounder level of representation in which the electron instead of being confined to a particular locality is distributed in a sort of probability haze all over the atom.