1
GATE EE 2023
MCQ (Single Correct Answer)
+1
-0.33

One million random numbers are generated from a statistically stationary process with a Gaussian distribution with mean zero and standard deviation $$\sigma_0$$. The $$\sigma_0$$ is estimated by randomly drawing out 10,000 numbers of samples ($$x_n$$). The estimates $${\widehat \sigma _1}$$, $${\widehat \sigma _2}$$ are computed in the following two ways.

$$\matrix{ {\widehat \sigma _1^2 = {1 \over {100000}}\sum\nolimits\limits_{n = 1}^{10000} {x_n^2} } & {\widehat \sigma _2^2 = {1 \over {9999}}\sum\nolimits\limits_{n = 1}^{10000} {x_n^2} } \cr } $$

Which of the following statements is true?

A
$$E(\widehat \sigma _2^2) = \sigma _0^2$$
B
$$E(\widehat \sigma _2^{}) = {\sigma _0}$$
C
$$E(\widehat \sigma _1^2) = \sigma _0^2$$
D
$$E(\widehat \sigma _1^{}) = E({\widehat \sigma _2})$$
2
GATE EE 2023
Numerical
+1
-0

Three points in the x-y plane are ($$-$$1, 0.8), (0, 2.2) and (1, 2.8). The value of the slope of the best fit straight line in the least square sense is _________ (Round off to 2 decimal places).

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3
GATE EE 2015 Set 1
MCQ (Single Correct Answer)
+1
-0.3
If a continuous function $$f(x)$$ does not have a root in the interval $$\left[ {a,b} \right],\,\,$$ then which one of the following statements is TRUE?
A
$$f\left( a \right).\,f\left( b \right) = 0$$
B
$$f\left( a \right).f\left( b \right) < 0$$
C
$$f\left( a \right).f\left( b \right) > 0$$
D
$$f\left( a \right)/f\left( b \right) \le 0$$
4
GATE EE 2014 Set 3
Numerical
+1
-0
The function $$f\left( x \right) = {e^x} - 1\,\,$$ is to be solved using Newton $$-$$ Raphson method. If the initial value of $${x_0}$$ is taken $$1.0,$$ then the absolute error observed at $${2^{nd}}$$ iteration is ___________.
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