各投保人是否出险互相独立,且出险的概率都是,记投保的10 000人中出险的人数为, 则。 (Ⅰ)记表示事件:保险公司为该险种至少支付10 000元赔偿金,则发生当且仅当, 2分
, 又, 故。························································································ 5分 (Ⅱ)该险种总收入为元,支出是赔偿金总额与成本的和。 支出 , 盈利 , 盈利的期望为 ,······································· 9分 由知,,
。
(元)。 故每位投保人应交纳的最低保费为15元。····················································· 12分 |