Mathematics and Machine Learning Fundamentals - Amazon_Ml_challenge OA Question

Company: Amazon_Ml_challenge

Difficulty: medium

Problem Statement

Question 1

Let P(x) = x³ - 6x² + 11x - 6. Which of the following is not a root of the polynomial?

Question 2

Let A = [[2, 1], [0, 3]]. What is A² (i.e., A × A)?

Question 3

Solve the inequality: (x-2) / (x+3) > 1

Question 4

Evaluate: ∫₀¹ (3x² + 2x) dx

Question 5

Given f(x) = x³ - 6x² + 12x, determine the x-coordinate(s) of any point of inflection.

Question 6

You are building a real-time fraud detection system where false negatives are very costly (i.e., missing a fraud is worse than wrongly flagging a transaction). Which model evaluation metric should you prioritize?

Question 7

Your model, trained on last year's customer data, starts performing poorly on recent transactions. Which of the following is the most likely cause?

Question 8

A box contains 4 red balls and 6 green balls. Two balls are drawn one after another without replacement. What is the probability that the second ball is red, given that the first ball was green?

Question 9

Let X be a discrete random variable with the following probability distribution: P(X = 1) = 0.2, P(X = 2) = 0.5, P(X = 3) = 0.3. What is the expected value of X?

Question 10

A test for a disease gives a false positive 5% of the time. The disease prevalence is 1%. If a person tests positive, what is the probability they actually have the disease? (Assume perfect sensitivity).

Question 11

A factory has two machines: Machine A produces 60% of the total items and has a defect rate of 2%. Machine B produces 40% of the total items and has a defect rate of 5%. If an item is found to be defective, what is the probability that it was produced by Machine A?

Question 12

In a chi-square goodness of fit test, the degrees of freedom is calculated as:

Question 13

For the following frequency distribution: | Class Interval | Frequency | | 0-10 | 2 | | 10-20 | 4 | | 20-30 | 6 | | 30-40 | 8 | What is the approximate standard deviation?

Question 14

In a Chi-square test, the test statistic is always:

Question 15

Which of the following metrics is most appropriate for evaluating a binary classification model on a highly imbalanced dataset?

Question 16

Which of the following techniques can be used for handling high-cardinality categorical features?

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