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5 votes

Expected Value Chi Square distribution

Your (5) "I changed $\frac{(n−1)s^2}{\sigma^2}∼\chi^2_{n-1}$ to $\frac{(n−1)s^2}{\chi^2_{n-1}}∼\sigma^2$" does not make much sense as $\sigma^2$ does not have a distribution while your $(n-...
Henry's user avatar
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2 votes

Expectation under convex order

The implication does not hold. For example, let $M \equiv 0$, $N$ be the Radamacher random variable (i.e., $P(N = \pm 1) = \frac{1}{2}$). Then for any concave function $u$, it follows by Jensen's ...
Zhanxiong's user avatar
  • 20.3k
1 vote

Distribution of outcomes of multiple binomial distributions

Let $S_i$, for $i=1,2,\ldots,50$, be the raw score for the $i$th subject, i.e. the number of tasks completed with the right hand. If $S_i \sim \mathrm{Bin}(30, 0.5)$, I'm assuming that you calculate ...
Doctor Milt's user avatar
  • 3,281

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