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This is not particularly different to any of the excellent answers which I have all upvoted. It did, however, prompt a limited comparison (benefiting from the workaround for bug in BenchmarkPlot here. Testing against @Mr.Wizard birthprob2 (just because I liked it): fun[n_, m_] := With[{rv = RandomInteger[{1, 365}, {m, n}]}, Total@(Boole[Length@Union[#] ...


For this problem you are likely better off performing a zillion simulations and determining the proportion of times that the product is greater than c. Below is described a brute-force way to obtain the desired probability for 2 and 3 variables. If c > 0 and with 2 random normal variables either both need to be positive or both need to be negative for ...


The joint density function of $x_b$ and $x_i$ can be written as f[xb_, xi_] := Piecewise[{{(1 - p)/2, xb == 0 && 3 <= xi <= 5}, {p/2, 3 <= xb <= 5 && 3 <= xi <= 5}}] Added May 12, 2015 * While I haven't been able to get Mathematica to display the joint density function from the TransformedDistribution function, that ...


It turns out this was a bug with version 10.0.2 of Mathematica. Upgrading to 10.1.0 resolved the issue and Mean@distInv now returns infinity.

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