1
GATE PI 2008
MCQ (Single Correct Answer)
+1
-0.3
For a random variable $$\,x\left( { - \infty < x < \infty } \right)\,\,$$ following normal distribution, the mean is $$\,\mu = 100\,\,.$$ If the probability is $$\,\,P = \alpha \,\,$$ for $$\,\,x \ge 110.\,\,\,$$ Then the probability of $$x$$ lying $$b/w$$ $$90$$ and $$110$$ i.e., $$\,P\left( {90 \le x \le 110} \right)\,\,$$ and equal to
A
$$\,1 - 2\alpha $$
B
$$\,1 - \alpha $$
C
$$1 - \alpha /2$$
D
$$2\,\alpha $$
2
GATE PI 2007
MCQ (Single Correct Answer)
+1
-0.3
The random variable $$X$$ takes on the values $$1,$$ $$2$$ (or) $$3$$ with probabilities $$\,{{2 + 5P} \over 5},{{1 + 3P} \over 5}\,\,$$ and $$\,\,{{1.5 + 2P} \over 5}\,\,$$ respectively the values of $$P$$ and $$E(X)$$ are respectively
A
$$0.05, 1.87$$
B
$$1.90, 5.87$$
C
$$0.05, 1.10$$
D
$$0.25, 1.40$$
3
GATE PI 2005
MCQ (Single Correct Answer)
+1
-0.3
Two dice are thrown simultaneously. The probability that the sum of numbers on both exceeds $$8$$ is
A
$${4 \over {36}}$$
B
$${7 \over {36}}$$
C
$${9 \over {36}}$$
D
$${10 \over {36}}$$
4
GATE PI 2005
MCQ (Single Correct Answer)
+1
-0.3
The life of a bulb (in hours) is a random variable with an exponential distribution $$\,\,f\left( t \right) = \alpha {e^{ - \alpha t}},0 \le t \le \infty .\,\,\,$$ The probability that its value lies $$b/w$$ $$100$$ and $$200$$ hours is
A
$$\,{e^{ - 100\alpha }} - {e^{ - 200\alpha }}$$
B
$${e^{ - 100}} - {e^{ - 200}}$$
C
$$\,{e^{ - 100\alpha }} + {e^{ - 200\alpha }}$$
D
$${e^{ - 100}} + {e^{ - 200}}$$
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