**Probability**

De Moivre pioneered the development of analytic geometry and the theory of probability by expanding upon the work of his predecessors, particularly Christiaan Huygens and several members of the Bernoulli family. He also produced the second textbook on probability theory, *The Doctrine of Chances: a method of calculating the probabilities of events in play*. (The first book about games of chance, Liber de ludo aleae ("On Casting the Die"), was written by Girolamo Cardano in the 1560s, but not published until 1663.) This book came out in four editions, 1711 in Latin, and 1718, 1738 and 1756 in English. In the later editions of his book, de Moivre gives the first statement of the formula for the normal distribution curve, the first method of finding the probability of the occurrence of an error of a given size when that error is expressed in terms of the variability of the distribution as a unit, and the first identification of the probable error calculation. Additionally, he applied these theories to gambling problems and actuarial tables.

An expression commonly found in probability is n! but before the days of calculators calculating n! for a large n was time consuming. In 1733 de Moivre proposed the formula for estimating a factorial as *n*! = *cn**n*+1/2e−*n*. He obtained an expression for the constant *c* but it was James Stirling who found that c was √(2*π*) . Therefore, Stirling's approximation is as much due to de Moivre as it is to Stirling.

De Moivre also published an article called Annuities upon Lives, in which he revealed the normal distribution of the mortality rate over a person’s age. From this he produced a simple formula for approximating the revenue produced by annual payments based on a person’s age. This is similar to the types of formulas used by insurance companies today. See also de Moivre–Laplace theorem

Read more about this topic: Abraham De Moivre

### Other articles related to "probability":

**Probability**- Relation To Randomness

... In a deterministic universe, based on Newtonian concepts, there would be no

**probability**if all conditions are known, (Laplace's demon) ...

**Probability**theory is required to describe quantum phenomena ...

... In

**probability**theory and statistics, the triangular distribution is a continuous

**probability**distribution with lower limit a, upper limit b and mode c, where a < b and a ≤ c ≤ b ... The

**probability**density function is given by whose cases avoid division by zero if c = a or c = b ...

... Aldona Aleškevičienė (Statulevičienė) –

**Probability**theory and stochastic processes Raimundas Bentkus –

**Probability**theory and stochastic processes Vidmantas Bentkus –

**Probability**... Paulauskas –

**Probability**theory and stochastic processes Vytautas Statulevicius –

**Probability**theory and stochastic processes Donatas Surgailis –

**Probability**...

... Obviously, the

**probability**of an employee being chosen in one quarter is 25 percent ... Marilyn's response was The

**probability**remains 25 percent, despite the repeated testing ... increases, but as long as the size of the pool remains the same, so does the

**probability**...

... Let X be a random sample from a

**probability**distribution with statistical parameters θ, which is a quantity to be estimated, and φ, representing quantities that are not ... Here Prθ,φ indicates the

**probability**distribution of X characterised by (θ, φ) ... is that the random interval (u(X), v(X)) covers the unknown value θ with a high

**probability**no matter what the true value of θ actually is ...

### Famous quotes containing the word probability:

“Legends of prediction are common throughout the whole Household of Man. Gods speak, spirits speak, computers speak. Oracular ambiguity or statistical *probability* provides loopholes, and discrepancies are expunged by Faith.”

—Ursula K. Le Guin (b. 1929)

“The *probability* of learning something unusual from a newspaper is far greater than that of experiencing it; in other words, it is in the realm of the abstract that the more important things happen in these times, and it is the unimportant that happens in real life.”

—Robert Musil (1880–1942)

“Only in Britain could it be thought a defect to be “too clever by half.” The *probability* is that too many people are too stupid by three-quarters.”

—John Major (b. 1943)