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Results tagged with self-study
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user 59395
A routine exercise designed to test one's knowledge; often from a textbook, course, or test used for a class or self-study. This community's policy is to "provide helpful hints" for such questions rather than complete answers.
3
votes
Finding a function minimizing the expected value
Interpreting the question as @whuber did in his comment, here is a quite vague hint:
https://en.wikipedia.org/wiki/Law_of_total_expectation
Edit after the spoilers: graphical illustration of the a …
5
votes
Accepted
Expectations of the geometric mean of a random sample from a uniform distribution
This is the same as finding
$$E[(X_1 X_2 \cdots X_n)^{1/n}],$$ where $X_i$ are independent and uniformly distributed. Hence it is equal to
$$E[X_1^{1/n}]\cdots E[X_n^{1/n}] = E[X_1^{1/n}]^n = \left(\ …