Page 206 - Engineering Mathematics Workbook_Final

Probability & Statistics

(a) 0 (b) 1/8 distribution on [0, 1]. The probability
P X + X  X  is the largest is
(c) 1/4 (d) 1/2 1 2 3
____. [GATE-2016 (CE-SET1)]
[GATE-2008-EE]
271. Assume that in a traffic junction, the
266. A random variable is uniformly cycle of the traffic signal lights is 2
distributed over the interval 2 to 10. minutes of green (vehicle does not
Its variance will be stop) and 3 minutes of red (vehicle

stops). Consider that the arrival time
(a) 16/3 (b) 6
of vehicles at the junction is
(c) 256/9 (d) 36 uniformly distributed over 5 minute
cycle. The expected waiting time (in
[GATE-2008 (IN)]
minutes) for the vehicle at the
267. The independent random variables X junction is _______
and Y are uniformly distributed in the [GATE 2017 – EE SESSION-1]
interval [-1, 1]. The probability that
max [X, Y] is less than 1/2 is EXPONENTIAL DISTRIBUTION

(a) 3/4 (b) 9/16 272. Assume that the duration in minutes
of a telephone conversation follows
(c) 1/4 (d) 2/3
the exponential distribution

[GATE-2012-EC, EE, IN] 1 − x /5
f ( ) x = e , x  0. The
5
268. Let X , X and X be independent probability that the conversation will
3
1
2
and identically distributed random exceed five minutes is
variables with the uniform
1
1
distribution on [0, 1]. The probability (a) (b) 1−
P X 1 e e
  is the largest is ______.
[GATE-2014 (EC-SET1)] (c) 1 (d) 1− 1
e 2 e 2
269. Suppose you break a stick of unit
length at a point chosen uniformly at [GATE-2007 (IN)]
random. Then the expected length of
the shorter stick is ____. 273. For a single server with Poisson
arrival and exponential service time,

[GATE-2016 (CE-SET1)] the arrival rate is 12 per hour. Which
one of the following service rates will
270. Let X , X and X be independent provide a steady state finite queue
2
1
3
and identically distributed random length?
variables with the uniform

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