Page 176 - Engineering Mathematics Workbook_Final

Probability & Statistics

73. For a single server with Poisson 77. If a random variable X has a Poisson
arrival and exponential service time, distribution with mean 5, then the
the arrival rate is 12 per hour. Which expectation
one of the following service rates will
provide a steady state finite queue E   ( X + ) 2  2
length?   equals
_____________.
(a) 6 per hour (b) 10 per hour

(c) 12 per hour (d) 24 per hour [GATE-2017-PAPER-2-CS]

[GATE-2017-ME-SESSION-2] 78. The cumulative distribution function
of a random variable x is the
74. Let X be a Gaussian random variable probability that X takes the value
2
mean 0 and variance  . Let Y =
max (X, 0) where max (a, b) is the (a) less than or equal to x

maximum of a and b. The median of (b) equal to x
Y is _______________.
(c) greater than x
[GATE-2017]
(d) zero [ESE-2017-EC]
75. The marks obtained by a set of

students are 38, 84, 45, 70, 75, 60, 48. 79. For a random variable x having the
The mean and median marks, PDF shown in the figure given below
respectively, are

(a) 45 and 75 (b) 55 and 48

(c) 60 and 60 (d) 60 and 70

[GATE-2017 (CH)]

76. The following sequence of numbers

is arranged in increasing order: 1, x, The mean and the variance are,
x, x, y, y, 9, 16, 18. Given that the respectively
mean and median are equal, and are
also equal to twice the mode, the (a) 0.5 and 0.66 (b) 2.0 and 1.33
value of y is
(c) 1.0 and 0.66 (d) 1.0 and 1.33

(a) 5 (b) 6
[ESE-2017-EC]
(c) 7 (d) 8
80. The probability density function
[GATE-2017 (CH)] F ( ) x = ae − b x , where x is a random

variable whose allowable value range

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