Question

Check whether the following is a p.d.f.

f(x) = 2  for 0 < x < q.

Answer 1

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.