Page 205 - Engineering Mathematics Workbook_Final

Probability & Statistics

Then the value of ‘a’ and Prob (c)    1 ,2  
X   0 , respectively, are   2   (d) {1, 2}

1 1 [ESE 2017 (EE)]
(a) 2, (b) 4,
2 2
263. The graph of a function f(x) is shown
1 1 in the figure.
(c) 2, (d) 4,
4 4

[GATE-2016 EC SET-3]

261. For a random variable x having the
PDF shown in the figure given below

The mean and the variance are,
respectively

For f(x) to be a valid probability
density function, the value of h is

(a) 1/3 (b) 2/3

(c) 1 (d) 3

[GATE 2018 (CE-AFTERNOON

SESSION)]
(a) 0.5 and 0.66 (b) 2.0 and 1.33
UNIFORM PROBABILITY
(c) 1.0 and 0.66 (d) 1.0 and 1.33 DISTRIBUTION

[ESE 2017 (EC)] 264. A point is randomly selected with
uniform probability in the x-y plane
262. A random variable X has a
probability density function with in the rectangle with corners at
(0, 0), (1, 0), (1, 2) and (0, 2). If p is
 kx e x ; x  0 the length of the position vector of
n −

f ( ) x =  (n is
 0; otherwise the point, then the expected value of

2
'
an integer) with mean 3. The values ' p is _________
of {k, n} are
[GATE 2004]
  1     1  
(a)  ,1 (b)  ,2 265. X is a uniformly distributed random
  2     4   variable that takes values between 0

3
E X
and 1. The value of ( ) will be

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