GATE Civil Engineering (CE) 2018 Shift 2 Solved Paper

Question : 30 of 65

Marks: +1, -0

The graph of a function

f(x)

is shown in the figure.

For

f(x)

to be a valid probability density function, the value of

h

Solution:

∫↙{0}↖{3} f(x) d x=1

∫↙{0}↖{1} f(x) d x+∫↙{1}↖{2} f(x) d x+∫↙{2}↖{3} f(x) d x=1

\;{h}/{2}+\;{2 h}/{2}+\;{3 h}/{2}=1

6 h=2 ⇒ h=\;{1}/{3}

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