1

GATE CSE 2017 Set 2

Numerical

+2

-0

If a random variable $$X$$ has a Poisson distribution with mean $$5,$$ then the expectation $$E\left[ {{{\left( {X + 2} \right)}^2}} \right]$$ equals _________.

Your input ____

2

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

3

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 ____

4

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 ____

Questions Asked from Probability (Marks 2)

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