Assuming α is known, find the maximum likelihood estimator of β
f(x;α,β) = , 1 ,,,,,,, .(xα.e-x/β)
,,,,,, ,,,,,,α!βα+1
I know that firstly you must take the likelihood of L(β). But unsure if I have done it correctly. I came out with the answer below...
Hi, I can't quite understand how to do this question please could someone help :)
Show, by the principle of superposition, that
u(x, t) =
∞
∑ An sin(npix)e2n2pi2t
n=1
where A1, A2,..., are arbitrary constants.
Thanks
Re: Seperation of Variables/ODE
Ignore my previous reply, I now have:
XT' = kX''T
divide both by kXT to get: T'/kT = X''/X
so T'/kT = µ and X''/x = µ (this is where G'(t)=k µG and F''(x)= µF is required)
now I am stuck on how to solve these.
Re: Seperation of Variables/ODE
I have began by :
XT' = kX''T
rearrange: T'/T=kX''/X=\alpha
trying to solve: T'/T=\alpha and kX''/X=\alpha
and that is the furthest I can go
The temperature distribution u(x, t), at time t > 0, along a homogeneous
metal rod can be obtained by solving the 1d heat equation;
ut = kuxx (1)
where k = 2 is a constant. The length of the rod is 1m and the temperature
at either end of the rod is zero for all time, so that the boundary...