Page 171 - Engineering Mathematics Workbook_Final

Probability & Statistics

38. A c ab was involved in a hit and run 40. The probability density function of a
accident at night. You are given the random variables x is
following data about the cabs in the x − 2

2 0
city and the accident. f ( ) x = 4 (4 x ) ; for 0 x  =
; otherwise
(i) 85% of cabs in the city are
green and the remaining cabs are The mean  of the random variable
blue. k
is __________
(ii) A witness identified the cab [GATE-2015-CE-SET-2, EE-SET-1, CS-
involved in the accident as blue.
SET-1]

(iii) It is known that a witness can 41. Consider the following probability
correctly identify the cab colour only mass function (p.m.f) of a random
80% of the time.
variable X.

Which of the following options is  q if X = 0
closest to the probability that the 
 
)
−
accident was caused by a blue cab? p ( , x q =  1 q if X = 1

 0 otherwise

(a) 12% (b) 15% 
If q = 0.4, the variance of X is
(c) 41% (d) 80%
_________
[GATE-2018-EC]
[GATE-2015-CE-SET-1]
39. A class of twelve children has two
more boys, than girls. A group of 42. The probability of obtaining at least
three children are randomly picked two ‘Six’ in throwing a fair dice 4
from this class to accompany the times is
teacher on a field trip. What is the (a) 425/432 (b) 19/144
probability that the group
accompanying the teacher contains (c) 13/144 (d) 125/432

more girls than boy?
[GATE-2015-ME-SET-1]
325
(a) 0 (b) 43. Let the random variable X represent
864 the number of times a fair coin needs

to be tossed till two consecutive
525 5
(c) (d) heads appear for the first time. The
864 12
expectation of X is _________.

[GATE-2018-EE] [GATE-2015]

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