alleryFind $k$ if $f(x) = kx$ for $0 < x < 2$ and 0 otherwise is a valid p.d.f.
A$1/2$
B$1/4$
C$1$
D$2$
Answer & Solution
Correct answer: A. $1/2$
$\int_0^2 kx\,dx = k[x^2/2]_0^2 = 2k = 1$ ⇒ $k = 1/2$.
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