GATE Electrical Engineering (EE) 2019 Solved Paper

Question : 31 of 65

Marks: +1, -0

The mean-square of a zero-mean random process is

\;{ {kT}}/{ {c}}

, where

{k}

is Boltzmann's constant,

{T}

is the absolut temperature, and

{c}

is a capacitance. The standard deviation of the random process is

Solution:

{V}( {x})= {E}[ {X}^{2}]-( {E}[ {X}])^{2}

Given

E[X^{2}]=\;{ {kT}}/{ {c}}

and

E[X]=0

Therefore,

V(x)=\;{k T}/{c}

and
Standard deviation

=√{V(x)}=√{\;{ {kT}}/{ {c}}}

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