Seems like you want to calculate an average of the counts, this is an nested aggregate. To achieve this you have to use a Derived Table:
SELECT avg(cnt)
FROM
(
SELECT CAST(EVENT_TIMESTAMP AS DATE) theDate,
COUNT(DISTINCT USER_ID) as cnt
FROM EventFct
WHERE CAST(EVENT_TIMESTAMP AS DATE) >'2014-05-10'
GROUP BY theDate
) as dt
Of course this eliminates the rows for each date, you might want to keep those rows and add the average as an additional column using a Windowed Aggregate Function:
SELECT CAST(EVENT_TIMESTAMP AS DATE) theDate,
COUNT(DISTINCT USER_ID) as cnt,
AVG(cnt) OVER () as avgcnt
FROM EventFct
WHERE CAST(EVENT_TIMESTAMP AS DATE) >'2014-05-10'
GROUP BY theDate