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The distribution of the capacity of multiple input multiple output (MIMO) fading depends on the joint distribution of the eigenvalues of a Wishart matrix, and is quite complex in general. We obtain here simple expressions for the distributions of the determinant of a Wishart matrix. Based on the distributions of the determinant and the trace of the Wishart matrix, we derive some simple and tight bounds on the complementary cumulative distribution function (CCDF) of the capacity of MIMO Rayleigh fading channels. The new bounds on capacity CCDF provide further insights into the channel capacity, and show the effects of the system parameters on the capacity distribution explicitly. These bounds can be used to evaluate the mean capacity as well.