Solution
= Solution
{c}
The condition $t>2$ guarantees a finite first moment. Direct integration gives
$$
\boxed{\mathbb E[X]=(t-1)\int_1^\infty x^{1-t}\,dx=\frac{t-1}{t-2}.}
$$
= Solution
{c}
The condition $t>2$ guarantees a finite first moment. Direct integration gives
$$
\boxed{\mathbb E[X]=(t-1)\int_1^\infty x^{1-t}\,dx=\frac{t-1}{t-2}.}
$$