Page 180 - Engineering Mathematics Workbook_Final

Probability & Statistics

E x
( )
(a) ( ) = E X 99. Let X be a random variable having
probability density function
V x
(b) ( ) V X= ( )  ax  x 

0

)
f ( , ,x x  =  x + 1 x 0

0
( )
V x 
(c) ( ) V X  0 x  x 0


( )
V x 
(d) ( ) V X [MS 2006] where   0, x  . If y = ln     X    
0
0
x
97. An archer makes 10 independent , then (Y  ) 3 is _______  0 
P
attempts at a target and his
probability of hitting the target at (a) e − 3 x 0 (b) 1 e − 3 x 0


−
5
each attempt is . Then the
−
6 (c) e − 3 (d) 1 e − 3
conditional probability that his last
two attempts are successful given that [MS 2007]
he has a total of 7 successful attempts 100. Independent trails consisting of
is _______ rolling a fair die are performed. The
probability that 2 appears before 3
1 7
(a) (b) (or) 5 is __________
5 5 15
1 1
7
25 8!     3 (a) (b)
1
5
(c) (d)     2 3
    
  
36 3!5! 6 6
   
1 1
[MS 2006] (c) (d)
4 5
k x
f
x
98. Let ( ) x = 4 , −  . [MS 2007]
(1+ ) x
101. Let X X ,........X be independent
,
6
2
1
Then the value of k for which f(x) is a random variables such that
probability density function is
_______ P ( X = − = P ( X = ) 1 = 1 ,
) 1
i
i
2
1 1 i = 1,2,............6. Then
(a) (b)
6 2  6 

P    X = 4 is ________.

i
(c) 3 (d) 6  i= 1 
[MS 2006] (a) 3 (b) 3
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