1

GATE CSE 2021 Set 1

MCQ (Single Correct Answer)

+2

-0.67

Consider the two statements.

S_{1} : There exist random variables X and Y such that

(E[X - E(X)) (Y - E(Y))])^{2} > Var[X] Var[Y]

S_{2} : For all random variables X and Y,

Cov[X, Y] = E [|X - E[X]| |Y - E[Y]|]

Which one of the following choices is correct?

2

GATE CSE 2021 Set 1

Numerical

+2

-0.67

The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter 2. For a randomly picked component of this type, the probability that, its lifetime exceeds the expected lifetime (rounded to 2 decimal places) is ______.

Your input ____

3

GATE CSE 2021 Set 1

Numerical

+2

-0.67

A sender (S) transmits a signal, which can be one of the two kinds: H and L with probabilities 0.1 and 0.9 respectively, to a receiver (R).

In the graph below, the weight of edge (u, v) is the probability of receiving v when u is transmitted, where u, v ∈ {H, L}. For example, the probability that the received signal is L given the transmitted signal was H, is 0.7.

If the received signal is H, the probability that the transmitted signal was H (rounded to 2 decimal places) is ______

Your input ____

4

GATE CSE 2020

Numerical

+2

-0.67

For n > 2, let a {0, 1}

Then, the probability that $$\sum\limits_{i = 1}^n {{a_i}{x_i}} $$ is an odd number is _______.

^{n}be a non-zero vector. Suppose that x is chosen uniformly at random from {0, 1}^{n}.Then, the probability that $$\sum\limits_{i = 1}^n {{a_i}{x_i}} $$ is an odd number is _______.

Your input ____

Questions Asked from Probability (Marks 2)

Number in Brackets after Paper Indicates No. of Questions

GATE CSE 2023 (1)
GATE CSE 2021 Set 1 (3)
GATE CSE 2020 (1)
GATE CSE 2019 (1)
GATE CSE 2018 (2)
GATE CSE 2017 Set 2 (3)
GATE CSE 2016 Set 2 (1)
GATE CSE 2016 Set 1 (1)
GATE CSE 2015 Set 3 (1)
GATE CSE 2015 Set 1 (2)
GATE CSE 2014 Set 2 (1)
GATE CSE 2014 Set 3 (1)
GATE CSE 2014 Set 1 (1)
GATE CSE 2012 (1)
GATE CSE 2011 (2)
GATE CSE 2010 (2)
GATE CSE 2009 (1)
GATE CSE 2008 (3)
GATE CSE 2007 (1)
GATE CSE 2006 (1)
GATE CSE 2005 (3)
GATE CSE 2004 (3)
GATE CSE 2002 (1)
GATE CSE 2001 (1)
GATE CSE 2000 (1)
GATE CSE 1999 (2)
GATE CSE 1996 (1)
GATE CSE 1995 (1)

GATE CSE Subjects

Discrete Mathematics

Programming Languages

Theory of Computation

Operating Systems

Computer Organization

Database Management System

Data Structures

Computer Networks

Algorithms

Compiler Design

Software Engineering

Web Technologies

General Aptitude