# All Questions

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### Estimating the radius of a circle

I have a circle iwth radius $r$. I want to test the hypothesis that $r \leq 2$ vs. $r >2$ based on the posterior of $r$. $r$ follows the prior distribution: $f(r) = \frac{2}{r^{2}}$, $r >0.5$. ...
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### proving $n!>2^n\;\;\forall \;n≥4\;$ by mathematical induction

My teacher proved the following $n!>2^n\;\;\;\forall \;n≥4\;$ in the following way Basis step: $\;\;4!=24>16$ ok Induction hypothesis: $\;\;k!>2^k$ Induction step: ...
### there is no bounded linear functional on $H$
let $H= L^2[0,1]$ and $C^1$ be the set of all continuouse functions on $[0,1]$ that have continuouse derivative.Let $t \in [0,1]$ and define $L: C^1 \longrightarrow F$ by $L (h)= h'(t)$. ...