1
Basics, jump to section 2 for the question :
I know that in the case of an exponential family with 1 parameter, meaning the distribution function of the sample variables can be written like :
$$ f_X(t) = \exp( \eta( \theta) T(t) - d( \theta) + S( x) ) $$
if we compare two hypothesis like those ...
"Natural parameter" links here. For the usage of this term in differential geometry, see differential geometry of curves.In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, based on some useful algebraic properties, as well as for generality, as exponential families are in a sense very natural sets of distributions to consider. The term exponential class is sometimes used in place of "exponential family", or the older term Koopman-Darmois family. The terms...
Problem of continuous real valued function
I don't understand Jim's comment on (b). He took $g(x)=f(x+1)-f(x)$. Why should there is a $c\in [0,1]$: $f(c)=f(c+1)$.
I can't apply mean value theorem here directly. Since given function need not be differentiable. I am not able to find a condition ...
