I'm having trouble with applying this theorem to likelihood functions in order to obtain a sufficiency statistic for the relevant variables.
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The factorisation theorem being:
Under certain regularity...
Homework Statement
Let f(x) = anxn + an-1xn-1 + ... + a1x + a0 be a polynomial where the coefficients an, an-1, ... , a1, a0 are integers.
Suppose a0 is a positive power of a prime number p.
Show that if \alpha is an integer for which f( \alpha ) = 0, \alpha is also a power of p.
Homework...
Try setting out a lab report like this:
Date/Title with page numbers
Begin with COSHH risk assessment (R phrases and S phrases to show you know what's going on)
Table of molecular weights, quantities, densities, structure and molar equivalents
Reaction Scheme
Write up procedure (mention...
I've been asked to synthesise this ferrocene based macrocycle (shown in picture below) starting from ferrocene and other available materials from Aldrich. I need to make sure molar equivalents are spot on with reagents. Can anyone help please?
So you could have B' = (1+z, 1+z^2, 1+z^3, 1+z^4, 1+z^5) for example or would this not work because the highest degree for R4[z] is 4?
Thanks for your reply.
Homework Statement
There is a standard basis, B = (1; z; z^2; z^3; z^4) where B is the basis of a R4[z] of real polynomials of at most degree 4.
I need to find another basis B' for R4[z] such that no scalar multiple of an
element in B appears as a basis vector in B' and also prove that...
Thanks for the reply.
I realized that I could use the substitution u^2 = 9cos^4(t)sin^2(t) + 9sin^4(t)cos^2(t)
Now taking out a factor of 9sin^2(t)cos^2(t) gave me:
u^2 = 9sin^2(t)cos^2(t) (cos^2(t) + sin^2(t))
and now you can use that cos^2(t) + sin^2(t) = 1
which now leaves...
Homework Statement
Find the total length of the curve t --> (cos^3(t), sin^3(t)), and t is between 0 and ∏/2 where t is in radians. Find also
the partial arc length s(t) along the curve between 0 and ∏/2
Homework Equations
The length is given by:
S = ∫\sqrt{xdot^2 + ydot^2} dt...