Page 175 - Engineering Mathematics Workbook_Final

Probability & Statistics
mean value of the random process at t
= 2 is __________.
[GATE-2017-EC-SESSION-2]
65. Assume that in a traffic junction, the
cycle of the traffic signal lights is 2
minutes of green (vehicle does not
stop) and 3 minutes of red (vehicle
stops). Consider that the arrival time
of vehicles at the junction is
uniformly distributed over 5 minute
cycle. The expected waiting time (in
minutes) for the vehicle at the
junction is _________
[GATE-2017-EE-SESSION-2]
66. The number of parameters in the
univariate exponential and Gaussian
distributions, respectively are
(a) 2 and 2 (b) 1 and 2
(c) 2 and 1 (d) 1 and 1
[GATE-2017-CE-SESSION-1]
67. Vehicles arriving at an intersection
from one of the approach roads
follow the Poisson distribution. The
mean rate of arrival is 900 vehicles
per hour. If a gap is defined as the
time difference between two
successive vehicle arrivals (with
vehicles assumed to be points), the
probability (up to four decimal
places) that the gap is greater than 8
seconds is _________.
[GATE-2017-CE-SESSION-1]
173
+
68. For the function ( ) x = a bx ,
f
0 x  1, to be a valid probability

density function, which one of the
following statements is correct?
(a) a = 1, b = 4 (b) a = 0.5, b = 1
(c) a = 0, b = 1 (d) a = 1, b = -1
[GATE-2017-CE-SESSION-1]
69. For a construction project the mean
and standard deviation of the
completion time are 200 days and 6.1
days respectively. Assume normal
distribution and use the value of
standard normal deviate z = 1.64 for
the 95% confidence level. The
maximum time required (in days) for
the completion of the project would
be _____________
[GATE-2017-CE-SESSION-2]
70. A six-face fair dice is rolled a large
number of times. The mean value of
the outcomes is _______.
[GATE-2017-ME-SESSION-1]
71. A sample of 15 data is as follows 17,
18, 17, 17, 13, 18, 5, 5, 6, 7, 8, 9, 20,
17, 3. The mode of the data is _
(a) 4 (b) 13
(c) 17 (d) 20
[GATE-2017-ME-SESSION-2]
72. The standard deviation of linear

dimensions P and Q are 3 m and

4 m respectively. When assembled,

the standard deviation (in m) of the
resulting linear dimension (P + Q) is
_______.
[GATE-2017-ME-SESSION-2]