Exercises
Multiple Choice
Articles
Open Problems
Login
24 items
Topic:
Probability
x
Start over
- to expand, or dig in by adding more tags and revising the query.
Sort By:
trending ▼
date
0
Undergraduate
By
Shiva Kintali
on Oct. 21, 2012 | Updated Dec. 6, 2017
Hat Check problem
Each of \(n\) customers gives a hat to a hat-check person at a restaurant. The hat-check person gives the hats back to the customers in a random order. What is the expected number of customers who g…
Mathematics
Probability
expectation
0
Undergraduate
By
Shiva Kintali
on Sept. 28, 2013 | Updated Jan. 4, 2018
Triangles in a random graph
Let \(G = G(n, \frac{1}{2})\) be a random graph on \(n\) vertices, i.e., for each pair of verices \(i, j\), we add the edge \((i, j)\) independently with probability \(\frac{1}{2}\). Let \(T_n\) be th…
Mathematics
Graph Theory
Probability
expectation
high probability
random graphs
triangles
variance
0
Undergraduate
By
Shiva Kintali
on Oct. 21, 2012 | Updated Dec. 6, 2017
Unbiasing a biased coin
Suppose that you want to output 0 with probability 1/2 and 1 with probability 1/2. At your disposal is a procedure BIASED-RANDOM, that outputs either 0 or 1. It outputs 1 with some probability \(p\) a…
Computer Science
Mathematics
Algorithms
Probability
expectation
0
Undergraduate
By
Shiva Kintali
on Sept. 28, 2013 | Updated Jan. 4, 2018
Basics of Expectation and Variance
If the random variable \(X\) takes values in non-negative integers, prove that: \(E[X] = \sum_{t=0}^\infty \Pr(X > t)\) Prove that if \(X_1\) and \(X_2\) are independent random variables then …
Mathematics
Probability
basics
expectation
variance
0
High School
By
True IITJEE
on Jan. 9, 2017 | Updated Jan. 3, 2018
JEE Advanced 2016 Paper 1 Mathematics Question 40
A computer producing factory has only two plants \(T_1\) and \(T_2\). Plant \(T_1\) produces 20% and plant \(T_2\) produces 80% of the total computers produced. 7% of computers produced in the factory…
Mathematics
Probability
conditional probability
jee
jee 2016
jee advanced
jee mathematics
0
Undergraduate
By
Shiva Kintali
on Oct. 21, 2012 | Updated Dec. 6, 2017
Number of inversions
Let \(A\) be an array of \(n\) distinct numbers. If \(i < j\) and \(A[i] > A[j]\), then the pair \((i,j)\) is called an inversion of \(A\). Design an algorithm that determines the number of inversio…
Mathematics
Probability
expectation
0
Undergraduate
By
Shiva Kintali
on May 22, 2013 | Updated Dec. 6, 2017
Basics of probability
Prove that, if \(E_1, E_2, \dots, E_n\) are mutually independent, then so are \(\overline{E_1}, \overline{E_2}, \dots, \overline{E_n}\) Give an example of three random events \(X,Y,Z\) for which any …
Mathematics
Probability
basics
conditional probability
0
Undergraduate
By
Shiva Kintali
on Oct. 3, 2013 | Updated Jan. 4, 2018
k-partite subgraph
For each \(k\in \mathbb{N}\) and each simple graph \(G=(V,E)\), prove that \(G\) has a \(k\)-partite subgraph \(H=(V',E')\) (i.e., \(H\) has chromatic number at most \(k\)) such that …
Mathematics
Graph Theory
Probability
graph coloring
probabilistic method
0
Undergraduate
By
Shiva Kintali
on Oct. 23, 2012 | Updated Dec. 6, 2017
Randomly assigned jobs
Suppose we have \(n\) jobs to distribute among \(m\) processors. For simplicity we assume that \(m\) divides \(n\). A job takes one step with probability \(p\) and \(k > 1\) steps with probability …
Mathematics
Probability
chernoff bound
0
Undergraduate
By
Shiva Kintali
on May 19, 2013 | Updated Dec. 6, 2017
Detecting fair coin
You are given two coins: one is a fair coin and the other is a biased coin that produces heads with probability 3/4. One of the two coins is picked, and is tossed \(n\) times. How many tosses suffic…
Mathematics
Probability
conditional probability
« previous
1
2
3
next page »
icon
Sign In or Sign Up
icon
Invite Friends
Post Something
x
Select What You'd Like To Post
POST AN ARTICLE
POST AN OPEN PROBLEM
POST AN EXERCISE
POST A MULTIPLE-CHOICE QUESTION
Content Types
Articles
Open Problems
Exercises
Multiple-Choice Questions
Levels
High school
Undergraduate
Graduate
Subjects
Mathematics
Computer Science
Puzzles
Optimization
Trending tags
infinite series
riemann zeta function
conditional expectation
derandomization
expectation
sat
counting
trees
equation
jee
Topics
Algebra
Algorithms
Approximation Algorithms
Calculus
Combinatorial Optimization
Combinatorics
Complexity Theory
Data Structures
Discrete Mathematics
Game Theory
Geometry
Graph Theory
Linear Algebra
Linear Programming
Logic
Mathematical Analysis
Mathematics
Matrix Theory
Number Theory
Optimization
Probability
Programming
Puzzles
Randomized Algorithms
Real Analysis
Trigonometry
×