Probability Fact
@ProbFact
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Daily tweets on probability from @JohnDCook .
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No, there’s a 50-50 chance two people share SOME birthday, not a PARTICULAR birthday.
if you're in a room with at least 23 people, there's a 50% chance that one of them shares your birthday
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Male heights have a normal distribution centered at 5' 10" with a standard deviation of 3 inches.
The probability of an 8 foot tall man is on the order of 1 in 1,000,000,000,000,000,000.
And yet there are men taller than 8'. The record is 8' 11".
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"Probability is the intersection of the most rigorous mathematics and the messiest of life." -- Nassim Taleb
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Discrete probability is conceptually easier than continuous probability because counting is easier than measure theory.
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'Probabilistic' comes from Latin. 'Stochastic' comes from Greek.
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Conditional probability is subtle. All probability is conditional. Therefore all probability is subtle.
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Next in the review queue: Bayesian Probability for Babies
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'There are only five probabilities the average human can handle: 99 percent, one percent, 100 percent, zero, and 50-50. That’s it.” — Richard Thaler
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Random phenomena are not obligated to follow one of the few dozen distributions that humans have given names to.
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'Probabilistic' comes from Latin. 'Stochastic' comes from Greek.
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'Probabilistic' comes from Latin. 'Stochastic' comes from Greek.
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If P(A | B) > P(A) then P(B | A) > P(B). If B makes A more likely then A makes B more likely.
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'Probabilistic' comes from Latin. 'Stochastic' comes from Greek.
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If P(A | B) > P(A) then P(B | A) > P(B). If B makes A more likely then A makes B more likely.
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The probability that two random integers are relatively prime is 6/π^2.
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'Probabilistic' comes from Latin. 'Stochastic' comes from Greek.
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'Probabilistic' comes from Latin. 'Stochastic' comes from Greek.
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Discrete probability is conceptually easier than continuous probability because counting is easier than measure theory.
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If P(A | B) > P(A) then P(B | A) > P(B). If B makes A more likely then A makes B more likely.
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'Monte Carlo is an extremely bad method; it should only be used when all alternative methods are worse.' -- Alan Sokal
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Uncorrelated random variables are not necessarily independent.
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Uncorrelated random variables are not necessarily independent.
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'Probabilistic' comes from Latin. 'Stochastic' comes from Greek.
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If P(A | B) > P(A) then P(B | A) > P(B). If B makes A more likely then A makes B more likely.
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Discrete probability is conceptually easier than continuous probability because counting is easier than measure theory.
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If P(A | B) > P(A) then P(B | A) > P(B). If B makes A more likely then A makes B more likely.
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If I flip a coin, look at the result, but don’t show you, its state is random for you but not for me. Probability describes knowledge.
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'Monte Carlo is an extremely bad method; it should only be used when all alternative methods are worse.' -- Alan Sokal
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Discrete probability is conceptually easier than continuous probability because counting is easier than measure theory.
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'... the theory of probabilities is at bottom only common sense reduced to calculus.' -- Pierre-Simon Laplace
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A random variable is a measurable function on a probability space.
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If P(A | B) > P(A) then P(B | A) > P(B). If B makes A more likely then A makes B more likely.
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One way to think of the Markov assumption: The future is independent of the past, given the present.
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Markov assumption: The future is independent of the past, given the present.
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If A makes B more likely, B makes A more likely.
P(B | A) > P(B) => P(A | B) > P(A).
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Information is quantified in terms of surprise. If everything in a message is expected, then it contains no information, no matter how long it is.
#informationtheory
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If P(A | B) > P(A) then P(B | A) > P(B).
If B makes A more likely then A makes B more likely.
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“It doesn’t matter that you’ve had 10 girls in a row. The chances that the next child is a boy are 50-50.”
Not necessarily.
🧵
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Uncorrelated random variables are not necessarily independent.
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'There are only five probabilities the average human can handle: 99 percent, one percent, 100 percent, zero, and 50-50. That’s it.” — Richard Thaler
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If P(A | B) > P(A) then P(B | A) > P(B). If B makes A more likely then A makes B more likely.
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Uncorrelated random variables are not necessarily independent.
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“There areonly five probabilities the average human can handle: 99 percent, one percent, 100 percent, zero, and 50-50. That’s it.” — Richard Thaler
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“A thing appears random only through the incompleteness of our knowledge.” -- Spinoza
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Uncorrelated random variables are not necessarily independent.
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'There are only five probabilities the average human can handle: 99 percent, one percent, 100 percent, zero, and 50-50. That’s it.” — Richard Thaler
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A normal random variable is within two standard deviations of its mean about 95% of the time.
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The standard deviations of independent random variables add like the sides of a right triangle.
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'Probabilistic' comes from Latin. 'Stochastic' comes from Greek.
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OH: "Not everything is Pareto distributed, but 80% of it is."
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Bayes theorem says the order in which you learn about two things doesn't matter.
P(A) P(B | A) = P(B) P(A | B)
You could first learn about A, and then learn about B given A, or you could first learn about B, then learn about A given B.
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The central limit theorem says that CDFs converge. The corresponding PDFs may not converge.
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Discrete probability is easier than continuous probability because counting is easier than measure theory.
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Discrete probability is conceptually easier than continuous probability because counting is easier than measure theory.
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'Probabilistic' comes from Latin. 'Stochastic' comes from Greek.
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'Monte Carlo is an extremely bad method; it should only be used when all alternative methods are worse.' -- Alan Sokal
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What probabilists call 'characteristic functions' everyone else calls Fourier transforms.
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One way to think of the Markov assumption: The future is independent of the past, given the present.
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It’s not very useful to say heights are not normally distributed. Nothing is exactly normally distributed.
It’s more useful to say how well the normal model fits, by what criteria, and under what conditions.
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If X has mean μ and variance σ², then (X - μ)/σ has mean 0 and variance 1.
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One way to think of the Markov assumption: The future is independent of the past, given the present.
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