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Mathematics
Mathematics
Problem
Show that the function
f
(
x
)
=
{
k
2
sin
(
k
x
)
for
0
≤
x
≤
π
k
0
otherwise
f(x) = \begin{cases} \frac{k}{2}\sin(kx) & \text{for } 0 \le x \le \frac{\pi}{k} \\ 0 & \text{otherwise} \end{cases}
f
(
x
)
=
{
2
k
sin
(
k
x
)
0
for
0
≤
x
≤
k
π
otherwise
is a probability density function for all
k
>
0
k > 0
k
>
0
.
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