f(alpha) exercise 1 solution
In the formula
alpha(q) = (Log(p
1
)*p
1
q
+ ... + Log(p
1
)p
N
q
)/(log(r)*(p
1
q
+ ... + p
N
q
))
note
0 < r < 1
and each
0 < p
i
< 1
so
Log(r) < 0 ,
each
Log(p
i
) < 0,
and each
p
i
q
> 0.
Consequently, the denominator is negative and each term of the numerator is negative.
That is, for each q, alpha(q) is positive.
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f(alpha) exercises
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