We introduce bivariate normal distribution operator for state vector |ψ〉 and find that its marginal distribution leads to one-dimensional normal distribution corresponding to the measurement probability |_λ,ν〈x|.ψ〉|², where |x〉_λ,ν is the coordinate-momentum intermediate representation. As a by-product, the one-dimensional normal distribution in statistics can be explained as a Radon transform of two-dimensional Gaussian function.