Random variable

Biology

Discrete mathematics

Statistics

Applied mathematics

Conditional probability distribution

Probability mass function

Conditional probability

Regular conditional probability

Distribution (mathematics)

Conditional expectation

Computer science

Limit (mathematics)

Limit of a function

Genetics

Random sequence

Database

Sequence (biology)

Mathematics

Mathematical analysis

Geometry

Measure (data warehouse)

Combinatorics

Point (geometry)

Theory of Probability and Its Applications

Let $X_1,X_2,\ldots$ be a sequence of independent random variables with common continuous distribution function~$F(x)$. Let~a be an arbitrary point of the support of the underlying probability measure. The present paper deals with random indices of those~X which approach point a from the left. Conditional distributions of such random variables are investigated and some limit laws for them are formulated.

Conditional Distributions of the Times of One-Sided Sequential Approximations