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For this probability model, As I am new to probability, I am looking for an approach of the underlying probability concept to work on the calculation in arriving at the expected winning prize of the total prize amount based on the Probability of not winning above 95% of the total prize and the Probability of winning above 95% of the total prize for each individual from my side.

I need an approach or any paper link on the model of this approach and not a final solution or entire calculation for this problem.

The expected winning prize amount should be based on both probabilities. Looking for a concept and not an actual final calculated number

Can I define the expected value of integral survival function as below ?

$\mathbb{E}Y=\int_{0}^{\infty}1-F_{Y}\left(x\right)dx$

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StatsUser
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    Please add the [tag:self-study] tag & read its [wiki](https://stats.stackexchange.com/tags/self-study/info). Then tell us what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. Please make these changes as just posting your homework & hoping someone will do it for you is grounds for closing. – kjetil b halvorsen Jun 01 '21 at 20:39
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    The expectation is the integral of the survival function (starting at zero). With data like this, that integral is the area of a bunch of rectangles (which you can easily see in a plot). So, consider starting with an accurate plot of the survival function and go on from there. – whuber Jun 05 '21 at 20:03
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    @whuber. I initially thought this was an elementary application of expected value and posted an erroneous 'hint' based on that. Having re-read the question, I realised that there were nuances to the problem that had eluded me and have removed this accordingly. Thank you for supplying clarity on this. – microhaus Jun 05 '21 at 20:20
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    Your modified question, which now asks about integrating the survival function, is answered in [several places here on CV](https://stats.stackexchange.com/search?tab=votes&q=integr*%20survival%20expect*). One full account is given at https://stats.stackexchange.com/questions/222478. – whuber Jun 06 '21 at 13:49
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    @whuber, thanks a lot for your link – StatsUser Jun 06 '21 at 16:08

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