1
GATE PI 2016
+2
-0.6
A normal random variable $$X$$ has the following probability density function $${f_x}\left( x \right) = {1 \over {\sqrt {8\pi } }}e{}^{ - \left\{ {{{{{\left( {x - 1} \right)}^2}} \over 8}} \right\}}, - \infty < x < \infty$$\$
Then $$\,\int\limits_1^\infty {{f_x}\left( x \right)dx = }$$
A
$$0$$
B
$${{1 \over 2}}$$
C
$${1 - {1 \over e}}$$
D
$$1$$
2
GATE PI 2015
+2
-0.6
A product is an assemble of $$5$$ different components. The product can be sequentially assembled in two possible ways. If the $$5$$ components are placed in a box and these are drawn at random from the box, then the probability of getting a correct sequence is
A
$${2 \over {5!}}$$
B
$${2 \over {5}}$$
C
$${2 \over {\left( {5 - 2} \right)!}}$$
D
$${2 \over {\left( {5 - 3} \right)!}}$$
3
GATE PI 2015
+2
-0.6
A coin is tossed thrice. Let $$X$$ be the event that head occurs in each of the first two tosses. Let $$Y$$ be the event that a tail occurs on the third toss. Let $$Z$$ be the event that two tails occur in three tosses. Based on the above information, which one of the following statements is TRUE?
A
$$X$$ and $$Y$$ are not independent
B
$$Y$$ and $$Z$$ are dependent
C
$$Y$$ and $$Z$$ are independent
D
$$X$$ and $$Z$$ are independent
4
GATE PI 2014
Numerical
+2
-0
A simple random sample of $$100$$ observations was taken form a large population. The sample mean and the standard deviation were determined to be $$80$$ and $$12,$$ respectively. The standard error of mean is ______.
GATE PI Subjects
Engineering Mechanics
Strength of Materials
Theory of Machines
Engineering Mathematics
Machine Design
Fluid Mechanics
Heat Transfer
Thermodynamics
Casting
Joining of Materials
Metal Forming
Machine Tools and Machining
Metrology
Industrial Engineering
EXAM MAP
Joint Entrance Examination