First names and Bayes theorem johndcook.com/blog/2023/04/0…

The F distribution is applied in analysis of variance (ANOVA).

Snedecor's F distribution is usually just called the F distribution, though 'F' is hard to search on by itself.

Uncorrelated random variables are not necessarily independent.

If you search a file of random bytes, what is the longest sequence of printable characters you'd expect to find?

johndcook.com/blog/2024/04/2…

Gamma distribution tail probability approximation johndcook.com/blog/2021/11/0…

If X and Y are independent exp rvs with the same mean, then X-Y is a double exp r.v.

If X has a gamma distribution with shape a and scale b, and c > 0, then cX has a gamma distribution with shape a and scale cb.

The minimum of two independent exponential rvs is an exponential rv.

The geometric mean of independent log-normal random variables has a log-normal distribution.

A binomial distribution may be approximated by a Poisson distribution. johndcook.com/blog/distribut…

Inverse Coupon Collector’s Problem
possiblywrong.wordpress.com/2024/04/16/inv…

The expected number of fixed points in a random permutation of n items is 1.

The harmonic mean of Cauchy random variables has a Cauchy distribution.

The sum of independent gamma random variables is a gamma random variable if each distribution has the same scale.

If Z is a standard normal rv, Z² has a chi-squared distribution with one degree of freedom.

Select a card at random from a standard deck and note its suit: ♣, ♦, ♥, or ♠.

Define the events A={♣,♦}, B={♣,♥}, and C={♣,♠}.

The events A, B, and C are pairwise independent but not independent.

Using dimensional analysis to check probability calculations johndcook.com/blog/2023/11/0…

Var(aX + bY) = a² Var(X) + b² Var(Y) + 2ab Cov(X, Y)

If X has a normal distribution, exp(X) has a log-normal distribution.