Short answers, pulled from the story.
The ensemble interpretation defines a pure state as describing the statistical properties of an ensemble of identically prepared systems rather than individual measurement outcomes. Leslie Ballentine established this modern framework in his 1970 paper The statistical interpretation of quantum mechanics to distinguish it from Copenhagen-like interpretations.
Max Born published his paper on quantum scattering theory in 1926 introducing the idea that particle motion follows probability laws while probability itself propagates via causal Schrödinger equations. He later described the statistical character of quantum mechanics as an empirical observation with deep philosophical implications during his Nobel Prize lecture in 1954.
Albert Einstein maintained consistently that quantum mechanics only supplied a statistical view and wrote in 1936 that the wave function does not describe a single system but rather relates to many systems or an ensemble. Karl Popper also argued around 1936 that the quantum state represented statistical assertions with no predictive power for individual particles.
Quantum observations are inherently statistical as seen in double slit experiments where electrons arrive at random times yet eventually form interference patterns. The ensemble approach rejects wave-particle duality doctrines in favor of definite particle trajectories and provides clear non-mysterious physical explanation through direct momentum transfer between particle and diffractive object.
An isolated quantum mechanical system evolves deterministically according to the Schrödinger equation though observation introduces randomness through interaction with measuring devices. Phase coherence between system and device breaks down when an individual system interacts with an observing device creating derived randomness described by the Born rule from two independent originative random processes.