wss process and autocorrelation

Question

In a paper, I saw a quiz question about auto-correlation of a WSS process than I can not understand. It says:

Let $X(t)$ be WSS. Which of the following can be correct?

• $a)$ $E[X(t_1) X(t_2)] = |t_1 - t_2|$

• $b)$ $E[X(t_1) X(t_2)] = \max\{t_1 - t_2,0\}$

• $c)$ $E[X(t_1) X(t_2)] = \max\{1- |t_1 - t_2|,0\}$

The correct answer is $c$.

Now I don't really understand it. In all three cases, the auto-correlation function depends only on the difference $t_1$ and $t_2$ so they all satisfy this condition.

Thanks in advance

Answer 1

Hint. Both (a) and (b) imply, when applied with $t_1 = t_2 := t$ that $X(t) = 0$ a. s. for all $t$. But this would imply that $E[X(t_1)X(t_2)] = 0$ for all $t_1, t_2$.