1

GATE CSE 2017 Set 2

MCQ (Single Correct Answer)

+2

-0.6

For any discrete random variable $$X,$$ with probability mass function $$P\left( {X = j} \right) = {p_j},$$

$${p_j}\,\, \ge 0,\,j \in \left\{ {0,..........,\,\,\,N} \right\},$$ and $$\,\,\sum\limits_{j = 0}^N {{p_j} = 1,\,\,} $$ define the polynomial function $${g_x}\left( z \right) = \sum\limits_{j = 0}^N {{p_j}{z^j}} .$$ For a certain discrete random variable $$Y$$, there exists a scalar $$\beta $$ $$ \in \left[ {0,1} \right]$$ such that $${g_y}\left( z \right) = {\left\{ {1 - \beta + \left. {\beta z} \right)} \right.^N}.$$ The expectation of $$Y$$ is

$${p_j}\,\, \ge 0,\,j \in \left\{ {0,..........,\,\,\,N} \right\},$$ and $$\,\,\sum\limits_{j = 0}^N {{p_j} = 1,\,\,} $$ define the polynomial function $${g_x}\left( z \right) = \sum\limits_{j = 0}^N {{p_j}{z^j}} .$$ For a certain discrete random variable $$Y$$, there exists a scalar $$\beta $$ $$ \in \left[ {0,1} \right]$$ such that $${g_y}\left( z \right) = {\left\{ {1 - \beta + \left. {\beta z} \right)} \right.^N}.$$ The expectation of $$Y$$ is

2

GATE CSE 2016 Set 2

Numerical

+2

-0

Suppose that a shop has an equal number of

**LED**bulbs of two different types. The probability of an**LED**bulb lasting more than $$100$$ hours given that it is of Type $$1$$ is $$0.7,$$ and given that it is of Type $$2$$ is $$0.4.$$ The probability that an**LED**bulb chosen uniformly at random lasts more than $$100$$ hours is _________.Your input ____

3

GATE CSE 2016 Set 1

Numerical

+2

-0

Consider the following experiment.

**Step1:**Flip a fair coin twice.**Step2:**If the outcomes are (TAILS, HEADS) then output $$Y$$ and stop.**Step3:**If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output $$N$$ and stop.**Step4:**If the outcomes are (TAILS, TAILS), then go to Step 1.The probability that the output of the experiment is $$Y$$ is (up to two decimal places) _____________.

Your input ____

4

GATE CSE 2015 Set 1

MCQ (Single Correct Answer)

+2

-0.6

Given Set $$\,\,\,A = \left\{ {2,3,4,5} \right\}\,\,\,$$ and Set $$\,\,\,B = \left\{ {11,12,13,14,15} \right\},\,\,\,$$ two numbers are randomly selected, one from each set. What is the probability that the sum of the two numbers equal $$16?$$

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 1 (2)
GATE CSE 2015 Set 3 (1)
GATE CSE 2014 Set 1 (1)
GATE CSE 2014 Set 3 (1)
GATE CSE 2014 Set 2 (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

Theory of Computation

Operating Systems

Algorithms

Database Management System

Data Structures

Computer Networks

Software Engineering

Compiler Design

Web Technologies

General Aptitude

Discrete Mathematics

Programming Languages