GATE Electrical Engineering (EE) 2021 Solved Papers

Question : 8 of 65

Marks: +1, -0

Let

X

be a continuous random variable denoting the temperature measured. The range of temperature is

[0,100]

degree Celsius and let the probability density function

X

f(x)=0.01

for

0 ≤ X ≤ 100

. Then mean of

X

is __________.

Solution:

PDF of

X

f(x)=0.01

for

0 ≤ x ≤ 100

PDF

{f}( {x})=0.01

for

0 ≤ {x} ≤ 100

E(x)=∫↙{0}↖{100} x f(x) d x=∫↙{0}↖{100} x(0.01) d x=\;{1}/{100}[\;{x^{2}}/{2}]_{0}^{100}=\;{100}/{2}=50

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