Page 172 - Engineering Mathematics Workbook_Final

Probability & Statistics

44. A fair die with faces {1, 2, 3, 4, 5, 6} value of the function ( ) x = e 3 /4 is
x
g
x
is thrown repeatedly till ‘3’ is _________. [GATE-2015-IN]
observed for the first time. Let X
denote the number of times the die is 49. Probability density function of a
thrown. The expected value of X is random variable x is given below:

_________.
 0.25 1 x  5
if 

[GATE-2015-EC-SET-3] f ( ) x =  0 otherwise


45. The variance of the random variable
X with probability density function P (x  ) 4 is

1 −
f ( ) x = x e x is ________. 3 1
2 (a) (b)
4 2

[GATE-2015-CS-SET-3]
1 1
(c) (d)
46. A random variable X has probability 4 8
density function f(x) as given below:
[GATE-2016-CE-SET-1]
 a bx for  1
0 x 
+

f ( ) x =  50. The spot speed (expressed in km/hr)
 0 otherwise observed at a road section are 66, 62,

45, 79, 32, 51, 56, 60, 53 and 40. The
If the expected value E[X] = 2/3, then
Pr[X < 0.5] is __________. median speed expressed in km/hr is
__________.
[GATE-2015-CS-SET-1]
[GATE-2016-CE-SET-2]
47. The probability that a thermistor

randomly picked up from a produced 51. A normal random variable X has the
unit is defective is 0.1. The following probability density function
probability that out of 10 thermistors   (x− ) 1   2  
randomly picked up, 3 are defective f ( ) x = 1 e −   8      ,− x
is x 8

(a) 0.001 (b) 0.057 −
Then 1  f x ( ) x dx ?
(c) 0.107 (d) 0.3
1
(a) 0 (b)
[GATE-2015-IN] 2

48. The probability density function of a 1
−
random variable X is ( ) x = e for (c) 1− (d) 1
x
P
e
x
x  0 and 0 otherwise. The expected
[GATE-2016 (PI)]

170