Page 174 - Engineering Mathematics Workbook_Final

Probability & Statistics
(a) Mean of f(x) and g(x) are same;
Variance of f(x) and g(x) are same.
(b) Mean of f(x) and g(x) are same;
Variance of f(x) and g(x) are
different.
(c) Mean of f(x) and g(x) are
different; Variance of f(x) and g(x)
are same.
(d) Mean of f(x) and g(x) are
different; Variance of f(x) and g(x)
are different.
[GATE-2016-CE-SET-2]
59. The probability that a screw
manufactured by a company is
defective is 0.1. The company sells
screws in packets containing 5 screws
and gives a guarantee of replacement
if one or more screws in the packet
are found to be defective. The
probability that a packet would have
to be replaced is ________.
[GATE-2016-ME-SET-2]
60. Let X , X and X be independent
1 2 3
and identically distributed random
variables with the uniform
distribution on [0, 1]. The probability
P ( X + 1 X  2 X 3 ) is largest is
_______.
[GATE-2016-CE-SET-1]
61. Shaquille O Neal is a 60% career free
throw shoots, meaning that he
successfully makes 60 free throws out
of 100 attempts on average. What is
the probability that he will
172
successfully make exactly 6 free
throws in 10 attempts?
(a) 0.2508 (b) 0.2816
(c) 0.2934 (d) 0.6000
[GATE-2016]
62. Passengers try repeatedly to get a seat
reservation in any train running
between two stations until they are
successful. If there is 40% chance of
getting reservation in any attempt by
a passenger then the average number
of attempts that passengers need to
make to get a seat reserved is _____.
[GATE-2017-EC-SESSION-2]
63. A person decides to toss a fair coin
repeatedly until he gets a head. He
will make at most 3 tosses. Let the
random variable Y denote the number
of heads. The value of var(Y), where
var(.) denotes the variance,
7 49
(a) (b)
8 64
(c) 7 (d) 105
64 64
[GATE-2017-EE-SESSION-2]
64. Consider the random process
+
X ( ) t = U Vt
where U is a zero-mean Gaussian
random variable and V is a random
variable uniformly distributed
between 0 and 2. Assume that U and
V are statistically independent. The