在贵阳市举办的第九届全国少数民族传统体育运动会的某个餐饮点上,遵义市某种茶饮料一天的销售量与该天的日平均气温(单位:℃)有关,若日平均气温不超过23℃,则日销售量为100瓶;若日平均气温超过23℃但不超过26℃,则日销售量为150瓶;若日平均气温超过26℃,则日销售量为200瓶.据气象部门预测,贵阳市在运动会期间每一天日平均气温不超过23℃,超过23℃但不超过26℃,超过26℃这三种情况发生的概率分别为P
1,P
2,P
3,又知P
1,P
2为方程5x
2-3x+a=0的两根,且P
2=P
3.
(1)求P
1,P
2,P
3的值;
(2)记ξ表示该茶饮料在运动会期间任意两天的销售量总和(单位:瓶),求ξ的分布列及数学期望.
考点分析:
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