1
GATE ECE 2014 Set 4
+1
-0.3
If calls arrive at a telephone exchange such that the time of arrival of any call is independent of the time of arrival of earlier or future calls, the probability distribution function of the total number of calls in a fixed time interval will be
A
Poisson
B
Gaussian
C
Exponential
D
Gamma
2
GATE ECE 2012
+1
-0.3
Two independent random variable X and Y are uniformly distributed in the interval [ - 1, 1]. The probability that max [X, Y] is less than 1/2 is
A
3/4
B
9/16
C
1/4
D
2/3
3
GATE ECE 2012
+1
-0.3
The power spectral density of a real process X(t) for positive frequencies is shown below. The value of $$E\,\left[ {{X^2}\,(t)} \right]$$ and $$E\,\left[ {X\,(t)} \right]$$, respectively, are
A
$$6000/\,\pi ,\,0$$
B
$$6400/\,\pi ,\,0$$
C
$$\,6400/\,\pi ,\,\,20\,\left( {\pi \sqrt 2 } \right)$$
D
$$\,6000/\,\pi ,\,\,20\,\left( {\pi \sqrt 2 } \right)$$
4
GATE ECE 2007
+1
-0.3
If E denotes expectation, the variance of a random variable X is given by
A
$$E\,\left[ {{X^2}} \right] - \,{E^2}\left[ X \right]$$
B
$$E\,\left[ {{X^2}} \right] + \,{E^2}\left[ X \right]$$
C
$$E\,\left[ {{X^2}} \right]$$
D
$${E^2}\left[ X \right]$$
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