Page 208 - Engineering Mathematics Workbook_Final

Probability & Statistics

(d) In a negatively skewed 283. Let U and V be two independent zero
distribution, mode > mean > median mean Gaussian random variables of
1 1
[GATE-2005] variances and respectively. The
4 9
280. The value of probability (3V  2U ) is
P

1    − x 2  
1
I = exp      dx is _____. (a) 4 (b)
2 0  8  9 2

[GATE 2006] 2 5
(c) (d)

281. The standard normal probability 3 9
function can be approximated as [GATE-2013 (EC)]

1 284. Let X be a zero mean unit variance
F ( X ) = ,
N
+
1 exp − ( 1.72555X N | X N | 0.12 ) Gaussian random variable. E[|X|] is
equal to ____.
where X = standard normal [GATE-2014-EC-SET 4]
N
deviate. If mean and standard
deviation of annual precipitation are 285. If f(x) is a continuous real valued
102 cm and 27 cm respectively, the random variable defined over the
probability that the annual interval (− ,+ ) and its occurance
precipitation will be between 90 cm is defined by the density function
and 102 cm is given as

 2

−
(a) 66.7% (b) 50.0% 1  1 x a     

f ( ) x = exp −      

(c) 33.3% (d) 16.7% 2 b   2   b    
where a and b are the statistical
[GATE-2008-CE]
attributes of the random variable {x}.
282. Let X be a random variable following The value of the integral
ND with mean +1 and variance 4. Let    2
−


Y be another normal variable with  a 1 exp − 1 x a         dx is



mean -1 and variance unknown. If − 2 b   2   b    
P ( X  − ) 1 = P (Y  ) 2 . The S.D. of
(a) 1 (b) 0.5
Y is _____. [GATE-2008]

(c)  (d) /2

[GATE-2014-CE-SET 2]

206