All Questions
Tagged with convexity binomial-distribution
2 questions
2
votes
1
answer
142
views
Proving convexity of the expected logarithm of binomial distribution
I would like to prove that the following function, for an arbitrary integer $n$:
\begin{equation}
\begin{split}
f(x) & =x\cdot E \ \log(1+\text{Binomial(n,x)}) \\
& = x \cdot \sum_{k=0}^{n} \...
- 23
2
votes
1
answer
183
views
Convexity of a function
Let: $F_{j+1,y}(s)$ be the cumulative distribution function of a binomial distribution with mean $y$, $j+1$ independent trials considered for $s$ successes. Is it possible to show in any way that:
$\...
