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LogLikelihood[ MultinomialDistribution[n, {p1, p2, p3, 1 - p1 - p2 - p3}], {{x1, x2, x3, x4}} ] This can be slightly cleaned up using FunctionExpand and FullSimplify to get rid of the binomials: FullSimplify[% // FunctionExpand, n == x1 + x2 + x3 + x4 && x1 >= 0 && x2 >= 0 && x3 >= 0 ...


2

As this is simple enough, you could use definitions : dist = MultinormalDistribution[{0, 0, 0}, IdentityMatrix[3]] ; prob[a_] = Integrate[PDF[dist, {z1, z2, z3}], {z2, -Infinity, Infinity}, {z3, -Infinity, Infinity}, {z1, a Sqrt[z2^2 + z3^2], Infinity}] (* ConditionalExpression[1/4 (2 - ...


3

First, let's find a in functional form: Probability[Abs[x] < a, x \[Distributed] NormalDistribution[]] which shows that f[a_] := Erf[a/Sqrt[2]] Now you want to solve for the a that has some probability, say 0.1. Then Solve[f[a] == 0.1, a] {{a -> 0.125661}} A little more generally: Solve[f[a] == p, a] {{a -> Sqrt[2] InverseErf[p]}} ...



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