1
GATE CSE 2017 Set 2
MCQ (Single Correct Answer)
+2
-0.6
$$P$$ and $$Q$$ are considering to apply for a job. The probability that $$P$$ applies for the job is $${1 \over 4},$$ the probability that $$P$$ applies for the job given that $$Q$$ applies for the job is $${1 \over 2},$$ and the probability that $$Q$$ applies for the job given that $$P$$ applies for the job is $${1 \over 3}.$$ Then the probability that $$P$$ does not apply for the job given that $$Q$$ does not apply for the job is
A
$${4 \over 5}$$
B
$${5 \over 6}$$
C
$${7 \over 8}$$
D
$${11 \over 12}$$
2
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 ____
3
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
A
$$N\beta \left( {1 - \beta } \right)$$
B
$$N\beta \left( {1 - \beta } \right)$$
C
$$N\left( {1 - \beta } \right)$$
D
Not expressible in terms of $$N$$ and $$\beta$$ alone
4
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 ____
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