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Question
Check whether the following is a p.d.f.
f(x) = 2 for 0 < x < q.
Solution
Here, f(x) > 0 `AA` x ∈[0, 1]
Now consider,
`int_0^1f(x)*dx`
= `int_0^1 2*dx`
= `2[x]_0^1`
= 2[1 – 0]
= 2 ≠ 1
f(x) is not p.d.f. of r.v.X.
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