Homeworks 1 PhD Course

Let X₁,X₂,...,Xn a statistical sample from the Poisson distribution, where the parameter is n. Show that the sample mean is sufficient statistics. 1. Let X₁,X₂,...,Xn a statistical sample from the Exponential distribution, where the parameter is n. Show that the sample mean is efficient statistics for 1/ n. 2. Let X₁,X₂,...,Xn a statistical sample from the N(m,s) distribution. If Mn denote the sample mean statistics, prove that Tn=(n/(n+1))* Mn is consistent estimation the of the parameter m. 3.