Page 204 - Engineering Mathematics Workbook_Final

Probability & Statistics

253. If a random variable X has a Poisson  0.2, for x  1

 
distribution with mean 5, then the f ( ) x =  0.1, for 1 x  4
 2 
expectation E  ( X + ) 2  equals  0, otherwise
  

_____.
The probability P(0.5 < X < 5) is
[GATE-2017 PAPER-2 (CS)] _____. [GATE-2014-EC-SET 2]

CONTINUOUS RANDOM VARIABLE 257. The variance of the random variable
X with probability density function
254. A probability density function is of 1
the form ( ) x = Ke −  x , x  (− , ) , f ( ) x = x e − x is _____.
p
2
the value of k is
[GATE-2015 (CS-SET 3)]
(a) 0.5 (b) 1
258. The probability density function of
(c) 0.5a (d) a − x
random variable X is ( ) x = e for
P
x
[GATE-2006] x  0 and 0 otherwise. The expected
value of the function ( ) x = e 3 / 4 is
x
g
255. Consider the continuous random x
variable with probability density _______.
function
[GATE-2015 (IN)]

f t = + −  259. Two random variables X and Y are
( ) 1 t for 1 t £ 0 = 1 – t

for 0 t  1 distributed according to

The standard deviation of the random  (x + y ), 0   1, 0   1
y
x

)
variable is f , x y ( , x y =  0, otherwise


1 1
(
(a) (b) The probability P X + Y  ) 1 is
3 6
_____.
1 1
(c) (d) [GATE-2016-EC-SET 2]
3 6
260. Let the probability density function of
[GATE-2006- ME]
a random variable, X, be given as:
256. Let X be a random variable with
−
probability density function f ( ) x = 3 e u ( ) x + ae u ( ) x−
3x
4x
x
2
where u(x) is the unit step function.

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