Use of SUM and COUNT with GROUP BY

I used this DDL+DML which is not like yours exectly

if OBJECT_ID('T','U') is not NULL drop table T
create table T(
        [State] varchar(10)
        ,[DOB] datetime
        ,[StartDt] datetime
        ,[EndDt] datetime
        ,[Desc] varchar(10)
        ,[Category] varchar(10)
        ,[MemberID] int
        ,[SubID] int
        ,[Code] int
)

insert T ([State],        DOB,          StartDt,                EndDt,          [Desc],   [Category], MemberID, SubID,  Code)
values
('NC',  '2003-01-30',   '2014-01-01',   '2014-01-31',   'Child',             'B',          123456,      2,      38),
('NC',  '2003-01-30',   '2014-01-01',   '2014-01-31',   'Child',             'B',          123456,      2,      39),
('NC',  '2003-01-30',   '2014-02-01',   '2014-05-31',   'Child',                 'B',      123456,      2,      38),
('NC',  '2003-01-30',   '2014-02-01',   '2014-05-31',   'Child',             'B',          123456,      2,      39),
('NC',  '2003-01-30',   '2014-06-01',   '2014-07-31',   'Child',             'B',          123456,      2,      38),
('NC',  '2003-01-30',   '2014-06-01',   '2014-07-31',   'Child',             'B',          123456,      2,      39),
('NC',  '2014-01-17',   '2014-01-01',   '2014-07-31',   'Infant',            'S',          456789,      1,      49),
('NC',  '2014-02-04',   '2014-02-01',   '2014-07-31',   'Infant',            'S',          246376,      3,      49)

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