Page 173 - Engineering Mathematics Workbook_Final

Probability & Statistics

52. The probability density function on 57. Let the probability density function of
2
the interval [a, 1] is given by 1/ x a random variable, X be given as:
and outside this interval the value of
the function is zero. The value of a is f ( ) x = 3 e u ( ) x + ae u −
−
3x
4x
( ) x
_____. x 2
[GATE-2016-CS-SET-1] where u(x) is the unit step function.
53. The second moment of a Poisson- Then the value of ‘a’ and Prob
distributed random variable is 2. The
mean of the random variable is X   0 , respectively. Are
___________
1 1
[GATE-2016] (a) 2, (b) 4,
2 2
54. Consider a Poisson distribution for
1
1
the tossing of a biased coin. The (c) 2, (d) 4,
mean for this distribution is  . The 2 4
standard deviation for this
distribution is given by [GATE-2016-EC-SET-3]

58. If f(x) and g(x) are two probability
2
(a)  (b) 
density functions,
(c)  (d) 1/ 

[GATE-2016-ME-SET-1]  x
x

55. Two random variables X and Y are  a + 1: − a   0

distributed according to f ( ) x =  x

x a

 − + 1: 0  
a

 (x + y ), 0   1,0   1 
y
x

)
x
f xy ( ,x y =  0, otherwise  − a : −   0
x
a



  x
 
x a
g ( ) x =  : 0  

P
The probability ( X + Y  ) 1 is __.  a
 0: otherwise

[GATE-2015-EC-SET-2] 


56. The area (in percentage) under
standard normal distribution curve of Which of the following statements is
true?
random variable Z within limits from
-3 to +3 is __________.
[GATE-2016-ME-SET-1]

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