申論題 - 阿摩線上測驗

申論題資訊

試卷：110年 - 110 國立高雄大學_碩士班招生考試_金融管理學系：統計學#102158
科目：研究所、轉學考(插大)◆統計學
年份：110年
排序：0

題組內容

≤≤≤≤6. Let N(t) , where 0 ≤ t ≤ T , denote a stochastic process, which satisfies the following conditions:
i. N (0)= 0 .
ii. N (t₂)- N (t₁) is normally distributed with mean 0 and variance t₂ - t₁ , where
0 ≤ t₁ < t₂ ≤ T .

iii. N(t) has independent increments. That is, given

are mutually independent.
Please answer the following question:

申論題內容

(1). (7%) Please evaluate the expectation of N(s)N(t) , where 0≤ s < t ≤ T . ( Hint: N(t)-N(s))+N(s)-N(0)))