A sequence of random variables x₁,…,x_n,… converges in mean squares to a random variable x if E[x²] and E[x_n²] exist and the expectation of the squared (Euclidean) distance between x_n and x converges to zero as n tends to infinity: ${\text{lim}}_{n\to \infty }E[{(x_n-x)}^2]=\text{0}.$ In particular, x can be a constant, x = θ‎. In this case convergence of x_n to θ‎ in mean squares is equivalent to the convergence of the bias and the variance of x_n to zero as n tends to infinity. Convergence in mean squares implies convergence in probability (the converse does not hold, in general). This is a particular case of convergence in the pth mean (or in L^p norm) defined as E[x^p], E[x_n^p] exist and ${\text{lim}}_{n\to \infty }E[{(x_n-x)}^p]=0.$ Convergence in pth mean implies convergence in rth mean for every r∈‎ (1, p).