Page 179 - Engineering Mathematics Workbook_Final

Probability & Statistics

90. A six-faced fair dice is rolled five 93. Type II error in hypothesis testing is
times. The probability (in %) of
obtaining “ONE” at least four times (a) acceptance of the null hypothesis
is when it is false and should be rejected

(b) rejection of the null hypothesis
(a) 33.3 (b) 3.33
when it is true and should be accepted
(c) 0.33 (d) 0.0033
(c) rejection of the null hypothesis

[GATE-2018-ME-MORNING when it is false and should be rejected
SESSION]
(d) acceptance of the null hypothesis
91. Let X , X be two independent when it is true and should be accepted
1
2
normal random variables with means [GATE-2016-SET-1]
 ,  and standard deviations  ,
1 2 1
 , respectively. Consider 94. Let X and Y are independent and
2
Y = X − X ; =  = 1, = 1, = 2 identically districted uniform random
1 2 1 2 1 2 variables over the interval (0, 1) and
. Then let S = X + Y. Find the probability

(a) Y is normally distributed with that the quadratic equation 9x-
mean 0 and variance 1 2 +9Sx+1=0 has no real root.

(b) Y is normally distributed with [MS 2005]

mean 0 and variance 5 95. Let E and F be two mutually disjoint

(c) Y has mean 0 and variance 5, but events. Further Let E and F be
is NOT normally distributed independent of G. If
( )
p = P E + ( ) P F and q = P(G),
(d) Y has mean 0 and variance 1, but then (E  
is NOT normally distributed P F G ) is _________

−
2
[GATE-2018-ME-MORNING (a) 1 pq (b) q + p
SESSION]
+
2
+
(c) p q (d) p q − pq
92. Let X , X , X and X be
3
2
1
4
independent normal random variables [MS 2006]
with zero mean and unit variance.
96. Let X be a continuous random
The probability that X is the
4 variable. With the probability density
smallest among the four is ________. function symmetric about O. If
( )   , then which of the
[GATE-2018-EC] V X
following statements is true?

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