By assuming various forms of interaction Hamiltonian the angular distribution of the decay products of spin 1/2 particle obeying the Dirac equation and that of spin 3/2 particle obeying Rarita-Schwinger equation are calculated. The ratio of the strength of parity conserving and the parity non- conserving interaction on the one hand and the asymmetry parameter α on the other hand is discussed. It is pointed out, that if the vector and pseudo-vector coupling in the universal Fermi weak interaction proposed by Feynman and Gell-Mann are exactly equal to each other, then this theory gives an asymmetry parameter α of Λ particle decay, which is consistent with the experimental result. If the ratio of the square of these two coupling constants is 1:1.55 as suggested by β-decay experiments, then the asymmetry parameter derived from this theory is -0.97, which is already on the margin of the experimental data. The angular distribution of the decay products of spin 3/2 particle obeying the Rarita-Schwinger wave equation cannot be made agree with the experimental result of the ∧ particle decay, a conclusion, which was first pointed out by Lee and Yang by using general arguments.