I have a random variable $1_{\{az_1+bz_i
What's the distribution function
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probability-theory
probability-distributions
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0conditional on $Z_1, \sum 1_{}$ is binomial, so you have a mixture of binomial, I haven't written down to see if you can explicitly do the mixing. – 2012-06-15
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0@mike : But the indicator functions being summed are not independent, since each of them involves $z_1$. – 2012-06-15
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0You've got a sum of Bernoulli-distributed random variables that are correlated. The correlations between pairs indexed by $i\neq j$ are all the same as each other if $i\neq 1\neq j$. The correlations between pairs indexed by $1$ and $i$ are all the same as each other. One hopes examining _pairwise_ dependences is enough, but I'm not sure it is. – 2012-06-15
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0@mike, you are right that's exactly the problem, I need the detailed solution. – 2012-06-15
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1I'm not sure where that discussion left us. Look at the sum, also, leave out the first, which has 2 $z_1$'s in it. The remainder is bin(n-1,p) with $p = \Phi(\frac {L - az_1}b)$. The probability of the sum being n-1 , for example is $\int \Phi(\frac {L - az}b)^{n-1} \phi(z) dz$. – 2012-06-15