Another way, f(x) = e^{3x}+\frac13 e^{-x}+\frac13 e^{-x}+\frac13 e^{-x} \ge \dfrac4{\sqrt[4]{27}} by AM-GM, with equality only when 3e^{4x}=1.

I think it must be 1+m-p=1 and mp=h^4 solving this we get m=\pm h^2 and p=\pm h^2

If one is familiar with the concepts of sufficiency and completeness, then this problem is not too difficult. Note that f(x; \theta) is the density of a \Gamma(2, \theta) random variable. The ...

Note ...

There is no difference, because D^{\alpha}(x(t)-x_0)=D^{\alpha}x(t)-D^{\alpha}x_0=D^{\alpha}x(t)

Simply note that T^2=I but T\ne I. This gives you the minimal polynomial of T. The characteristic polynomial has the same irreducible factors as the minimal polynomial and degree equal to the ...