Re: normal and binomial distribution

marko.suonpera@xxxxxxxxxxxxx wrote:
Suppose X_i = 0 with probability P, and ~N(µ,σ²) with probability (1-
P). Then what is the distribution of

Y = sum(i=1...N, X_i) ?

BR, Marko

I assume you intend the X_i to be independent? Let B be the number of X_i drawn from the normal distribution; then B is binomial and the conditional distribution of Y given B is normal. From that you can write down the c.d.f. of Y as a sum of normal c.d.f.s plus an extra term for the case B = 0. I rather doubt this turns out to be a well-known distribution, particularly since the c.d.f. of Y has a jump discontinuity at zero.

HTH,
Paul
.

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