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GATE 2019: Engineering Mathematics Test 9

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Question 1

In an experiment with 15 observations on x, the following results we available

One observation that was 20 was found to be wrong and was replaced by the correct value 30. Then the corrected variance is ______.

Question 2

A continuous random variable X constrained to only positive values 0 < x < ∞, the maximum entropy if is

Question 3

Let X and Y are independent random variable. Given that X has a uniform distribution over –1 ≤ x ≤ 1 and Another random process W(t) is defined as W(t) = (Y + 3Xt) t
The mean square value of W(t) is

Question 4

Assume that in a traffic junction, the cycle of the traffic signal lights is 2 minutes of green (vehicle does not stop) and 3 minutes of red (vehicle stops). Consider that the arrival time of vehicles at the junction is uniformly distributed over 5 minute cycles. The expected waiting time (in minutes) for the vehicle at the junction is ________.

Question 5

Let X be a random variable with probability density function

The probability p(0.5<x<5) is ________

Question 6

Two independent random variables X and Y are uniformly distributed in the interval [–1, 1]. The probability that max [X, Y] is less than 1/2 is
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Aug 23ESE & GATE EE