does it make sense to ask the expected value for discrete values in non-enumerable sets?

Asked Jun 10 '18 at 04:39

Active Jun 10 '18 at 04:39

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I want to know, is this question well formulated? If so, what is the answer?

"Let randomly choose n numbers in a range [0,1], what is the expected value of the smallest number? if distribution function is uniform."

What is confusing me is "the probability of this event can be given by a distribution function"? Please help me

asked Jun 10 '18 at 04:39

It sounds like you have independent and identically distributed (i.i.d.) random variables ${X_1, X_2, ..., X_n}$, each uniformly distributed over $[0,1]$, and you want to find $E[\min[X_1, ..., X_n]]$. – Michael Jun 10 '18 at 04:56
I think that's precisely it – Jun 10 '18 at 05:37
Read this answer and the comment. – A.Γ. Jun 10 '18 at 05:47
In general, for mins and maxes you can use things like: $${\min[X_1, ..., X_n] > x} = {X_1>x}\cap {X_2>x}\cap \cdots \cap {X_n>x}$$ – Michael Jun 10 '18 at 05:51

does it make sense to ask the expected value for discrete values ​in non-enumerable sets?