1. **Problem Statement:** We are given a stochastic process $\{N(t): t \geq 0\}$ which is a Poisson process. We need to determine if the statement "$N(t)$ has independent and non-stationary increments" is true or false. 2. **Recall the definition of a Poisson process:** - A Poisson process $N(t)$ has **independent increments**, meaning the number of events occurring in disjoint time intervals are independent. - It also has **stationary increments**, meaning the distribution of the number of events in any time interval depends only on the length of the interval, not on its position. 3. **Key properties:** - **Independent increments:** For any $0 \leq s < t$, the increment $N(t) - N(s)$ is independent of the past. - **Stationary increments:** The distribution of $N(t) - N(s)$ depends only on $t - s$. 4. **Evaluate the statement:** - The statement claims $N(t)$ has independent increments — this is **true**. - The statement claims $N(t)$ has **non-stationary** increments — this is **false** because Poisson processes have stationary increments. 5. **Conclusion:** The statement is **false** because although $N(t)$ has independent increments, it does not have non-stationary increments; its increments are stationary. **Final answer:** The statement is **False**.