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This paper summarizes the scientific activity of de Finetti in probability and statistics. It falls into three sections: Section 1 includes an essential biography of de Finetti and a survey of the basic features of the scientific milieu in which he took the first steps of his scientific career; Section 2 concerns de Finetti's work in probability: (a) foundations, (b) processes with independent increments, (c) sequences of exchangeable random variables, and (d) contributions which fall within other fields; Section 3 deals with de Finetti's contributions to statistics: (a) description of frequency distributions, (b) induction and statistics, (c) probability and induction, and (d) objectivistic schools and theory of decision. Many recent developments of de Finetti's work are mentioned here and briefly described.

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Let p be a random probability measure chosen by a Dirichlet process whose parameter α is a finite measure with support contained in 0 +∞ and suppose that V = x 2 p dx − xp dx 2 is a (finite) random variable. This paper deals with the distribution of V, which is given in a rather general case. A simple application to Bayesian bootstrap is also illustrated.

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