Billiard table manufacturers have produced convertible billiard tables (in the broad sense) that double as dining tables or as table tennis, foosball, or air hockey, tables, with removable hard tops. Home pool tables, which often lack a ball-return system, are commonly either 4 × 8 ft or 3.5 × 7 ft models, a medium between 3 × 6 ft. bar/pub tables and 4.5 × 9 ft tournament-size models. Low-end tables tend toward the smaller range, and may have MDF or wood beds as an alternative to slate; those with light-weight beds may be foldable for storage, as with table tennis. Miniature tables
Normally distributed and uncorrelated does not imply independent Normally distributed and uncorrelated does not imply independent In probability theory, although simple examples illustrate that linear uncorrelatedness of two random variables does not in general imply their independence, it is sometimes mistakenly thought that it does imply that when the two random variables are normally distributed. This article demonstrates that assumption of normal distributions does not have that consequence, although the multivariate normal distribution, including the bivariate normal distribution, does. To say that the pair ("X", "Y") of random variables has a bivariate normal distribution means that every constant (i.e. not random) linear combination "aX" + "bY" of "X"