The distribution of molecular weight (MW) and composition of diblock copolymers is considered theoretically. Assuming that the chain end of each block is coupled randomly, the weight-average MW of the block copolymers is given by M w = w 1 (M w,1 + M n,2 ) + w 2 (M w,2 + M n,1 ), irrespective of the shape of the distribution of each block, where w i is the weight fraction, and M n,i and M w,i are the number- and weight-average MW of each block. In copolymer chains, the chemical compositions as well as the MWs cannot be identical for all polymers, and there exists a bivariate distribution of MW and composition. When the MW distribution (MWD) of both blocks follows the Schulz-Zimm distribution, the bivariate distribution can be obtained analytically. In addition to the bivariate distribution, the full MWD, the average composition as a function of MW, the composition distribution of copolymers having a specified MW, and the overall composition distribution are obtained. The composition distribution, as well as the average composition, becomes independent of MW under the condition σ 1 /M n,1 = σ 2 /M n,2 , where σ i is a parameter indicating the narrowness of the Schulz-Zimm distribution. The present theoretical analysis provides new insight into the design of diblock copolymers.