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 Nov 19 comment Deciding whether or not an exponentially distributed random variable exists in a set via the use of a “black box” function I was thinking to use some sort of Bayesian inference scheme, but if there is a simpler method... Nov 19 comment Deciding whether or not an exponentially distributed random variable exists in a set via the use of a “black box” function @fedja Provided a sufficient number of samplings, is there a known "best" method of deciding whether the element $x_q$ exists in $X$? Nov 19 comment Deciding whether or not an exponentially distributed random variable exists in a set via the use of a “black box” function @fedja I can probably afford something like ~10^5 samplings, though I'd be interested in what theory has to say regardless of feasibility. Nov 19 revised Deciding whether or not an exponentially distributed random variable exists in a set via the use of a “black box” function added 36 characters in body Nov 19 comment Deciding whether or not an exponentially distributed random variable exists in a set via the use of a “black box” function @fedja Ah, $R$ is defined earlier as the set of rate parameters associated with the exponentially distributed random variables in $X$. Nov 19 comment Deciding whether or not an exponentially distributed random variable exists in a set via the use of a “black box” function @fedja I have added some specifications for $N$ and $w$ in Note 2. I can tighten them as needed. $R - \lambda_q$ is meant to be the set $R$ without the element $\lambda_q$ (perhaps this notation is incorrect?) Nov 19 revised Deciding whether or not an exponentially distributed random variable exists in a set via the use of a “black box” function added 76 characters in body; added 34 characters in body Nov 19 revised Deciding whether or not an exponentially distributed random variable exists in a set via the use of a “black box” function added 73 characters in body Nov 18 revised Deciding whether or not an exponentially distributed random variable exists in a set via the use of a “black box” function added 132 characters in body Nov 18 revised Deciding whether or not an exponentially distributed random variable exists in a set via the use of a “black box” function added 14 characters in body Nov 18 comment Deciding whether or not an exponentially distributed random variable exists in a set via the use of a “black box” function @Anthony Quas Fair point. I am looking for a bound in terms of $N$, and I have changed the question to specify that we know $N$. Nov 18 awarded Editor Nov 18 revised Deciding whether or not an exponentially distributed random variable exists in a set via the use of a “black box” function added 24 characters in body Nov 17 awarded Student Nov 17 asked Deciding whether or not an exponentially distributed random variable exists in a set via the use of a “black box” function