Page 182 - Engineering Mathematics Workbook_Final

Probability & Statistics

lnU up tails) = P (both coins show up
107. If Y = 1 , where U
lnU + 1 ln − (1 U 2 ) 1 heads) then u + v = _________

and U are independent U (0, 1) 1 1
2 (a) (b)
random variables, then variance of Y 4 2
= _________
3
(c) (d) 1
1 1 4
(a) (b)
12 3
[MS 2010]
1 1
(c) (d) 111. Let X be a discrete random variable
4 6 with

[MS 2009] 2 e − 1   1   K+ 2 2
P ( X = K ) =  +      ,
108. If X is a Binomial (30, 0.5) random 3 K !  3  3
variable, then _________ K = 0, 1, 2, ……., Let E = {0, 2, 4,
…..}. Then ( X  E ) =
P
P
(a) ( X  15 = ) 0.5 ___________

P
(b) ( X  15 = ) 0.5 5 2 5 1
1
−
−
1
(a) + e (b) + e
12 3 12 3
P
(c) ( X  15  ) 0.5
7 1 7 1
−
−
1
1
(c) − e (d) + e
P
(d) ( X  15  ) 0.5 [MS 2009] 12 3 12 3
109. Let E and F be two events with [MS 2010]
( ) 0, (F E =
P E  P / ) 0.3 and
112. If X and X are identical
1
2
=
P E
P ( E  F C ) 0.2 then ( ) = independent random variables N (0,
2
2
___________ 1), then ( X + X  ) 2 =______
P
1
2
1 2 − −
2
1
(a) (b) (a) e (b) e
7 7
−
1
−
(c) 1 e (d) 1 − −2
4 5
(c) (d)
7 7 [MS 2010]
[MS 2010] 113. Let X and X be identical
1
2
independent random variables Exp
110. Two coins with probability of heads u
P
and v respectively, are tossed (3). Then ( X + X  ) 1 = _______
1
2
independently. If P(both coins show

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