Okko: Техническое собеседование

A probability space is (Omega, F, P): outcomes, measurable events and a probability measure. A measure-zero set has P(A)=0; under continuous distributions, individual points and countable unions of points can have zero probability.

A probability space consists of three parts. Omega is the sample space of possible outcomes. F is a sigma-algebra of events we are allowed to assign probabilities to. P is a probability measure on F with P(Omega)=1, P(empty)=0 and countable additivity.

The sigma-algebra matters because for continuous spaces not every arbitrary subset is well-behaved under a measure. It is closed under complements and countable unions, which lets probability operations remain consistent.

A set of measure zero is an event with probability zero. In a continuous distribution over R, a single exact point has probability zero, and any countable set of points also has probability zero by countable additivity. This does not mean the event is logically impossible; it means it carries no probability mass under that measure.

A vector space supports vector addition and scalar multiplication with the usual axioms. A span is all linear combinations of a set of vectors; a basis is a linearly independent set whose span is the whole space.

A vector space is a set of objects where you can add two vectors and multiply a vector by a scalar while satisfying closure, associativity, distributivity, identity and inverse properties.

The linear span of vectors v1...vk is the set of all linear combinations a1 v1 + ... + ak vk. It can be the whole space or a subspace.

A basis is a stronger object. It spans the target space and its vectors are linearly independent. Linear independence means no basis vector can be represented as a linear combination of the others. Because of that, every vector in the space has a unique coordinate representation in that basis.

Under common regularity conditions, the normalized sample mean tends to a normal distribution as sample size grows. This justifies normal approximations for confidence intervals, tests and experiment readouts.

The Central Limit Theorem says that for independent identically distributed variables with finite variance, the distribution of the normalized sample mean approaches a normal distribution as sample size grows:

(mean - mu) / (sigma / sqrt(n)) -> N(0, 1).

This is important because many metrics are averages or proportions. Even if individual observations are not normally distributed, the sampling distribution of the mean can be approximately normal for large n. That gives practical formulas for standard errors, confidence intervals and hypothesis tests.

In A/B testing, CLT reasoning underlies z-tests and t-test approximations for many user-level metrics. The assumptions still matter: independence, finite variance, enough sample size and a metric definition that does not create severe dependence or heavy-tail instability.

REST is commonly HTTP/resource-oriented and often JSON/text based; gRPC uses protobuf contracts over HTTP/2 and supports efficient binary RPC and streaming. Database indexes speed lookups by maintaining auxiliary structures such as B-trees for ranges or hash indexes for equality.

REST is an architectural style commonly implemented over HTTP with resource URLs, methods such as GET/POST and JSON payloads. It is simple, widely interoperable and human-readable, but may be less efficient for high-throughput service-to-service RPC.

gRPC defines service methods and message schemas with protobuf, usually runs over HTTP/2, uses compact binary serialization and supports streaming. It is useful for internal microservice communication where typed contracts, lower payload overhead and long-lived connections matter.

A database index is an auxiliary data structure that lets the database find rows without scanning the whole table. For equality lookup, a hash table-like structure can work. For range queries, sorting and ordered traversal matter, so B-tree/B+tree-style indexes are common. The trade-off is write overhead and extra storage because the index must be maintained when data changes.