Банк вопросов из реальных собеседований

A fair coin is tossed 10 times. What is the probability of getting exactly 6 heads?

There are 100 dogs and 100 cats. 50 dogs and 40 cats weigh more than 5 kg. Let B - the animal is a cat, A - the animal weighs more than 5 kg. Find P(A | B).

Why do they use BatchNorm? How does it work during training and how does the behavior differ on inferencing?

How to solve a probability problem with a large number of independent identical tests?

How are PDF, CDF, fitting distributions and Bayes' theorem related?

A coin has unknown heads probability p. You observe n tosses and k heads. Derive the maximum likelihood estimate for p.

Why does the high accuracy of a medical test not guarantee a high probability of illness after a positive result?

How to calculate the probability of at least one head in 10 tosses of a fair coin?

What is a vector space? What is the difference between a linear span and a basis?

What is a probability space? What is a set of measure zero and why can a finite or countable set have probability zero in a continuous distribution?

Explain the law of large numbers and the central limit theorem. What distribution do you get if you repeatedly take samples of 100 observations and compute their mean?

In a series of coin tosses, the eagle fell H times and the tails T times. How can the maximum probability method be used to estimate the probability of eagle falling p and check that the maximum is found?

Explain BatchNorm for image tensors, what changes at inference, and what must be synchronized in multi-GPU training.

To what values does the temperature apply, how does it change the distribution after softmax and how does it differ from the method of selecting a token?

How can an analytical solution of linear regression be obtained by the method of least squares, when it is not applicable and under what assumptions the method of maximum probability gives the same result?