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
Theory of Machines
Machine Design
Fluid Mechanics
Thermodynamics
Casting
Joining of Materials
Metal Forming
Machine Tools and Machining
Metrology
Industrial Engineering
EXAM MAP
Medical
NEET