You need 1 1/4" of subfloor. Typically it is 3/4" of plywood or OSB and 1/2" of mudbase or cement board.
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No, plywood alone is not strong enough for ceramic tile. These floors require a very sturdy subfloor at least 1 1/4" thick before the tile. This requires either using cement board or a pored mudbed.
Not very thick. Many building codes (perhaps most) allow 3/4 inch waferboard or 5'8 inch plywood as the structural subfloor over 16" O.C. joists. This is fine for normal sized floors with carpet or vinyl overlay, but is insufficient for very large floors or floors to be finished in ceramic, slate or porcelain tiles.
The average thickness of an American house floor is about one inch. This would include the subfloor and any time of other floor covering.
The sub floor should not be a problem if it hasn't been one for other reasons. What is most important is the installation of cement board over the sub floor to keep the tile and grout from cracking. Most marble tile used in residential buildings is not so heavy as to create weight issues.