Hudson River Trading数据相关面经_Hudson River Trading数据相关面试真题及高频题

1.Finding Conditional Probability

2.Probability of Painted Cube Face

3.Probability of Matching Balls in Boxes

4.Expected Number of Intersections in Random Walk

5.Expected Number of Handshakes

6.Probability of Coin Toss Outcome

7.Expected Sum of Dice Rolls

8.Probability of Dice Roll and Coin Toss

9.Dice Expectation Problem

10.Probability Comparison between Dice and Coin Outcomes

1. Finding Conditional Probability

The joint probability is given by f(x, y) = 8x^2 + 2xy, where 0 < x < 1 and 0 < y < 1. Find P(Y < X).

2. Probability of Painted Cube Face

A 3x3x3 white cube has its surface painted red. A cube is randomly chosen and thrown onto a table, showing five white faces. What is the probability that the remaining face is red?

3. Probability of Matching Balls in Boxes

Three boxes contain two balls each: one has two blue balls, one has a blue and a red ball, and one has two red balls. If a randomly chosen ball from a randomly chosen box is blue, what is the probability that the other ball in the same box is also blue?

4. Expected Number of Intersections in Random Walk

Consider a random walk on the boundary of a circle centered at the origin, starting from 0° and taking n steps. Each step is a random move on the boundary, and straight lines connect consecutive points. What is the expected number of intersections among these lines?

5. Expected Number of Handshakes

There are a people from group A and b people from group B, seated around a circular table in random order. Adjacent colleagues of the same group shake hands. Find the expected total number of handshakes.