Question

2. In your pocket is a random number N of coins, where N has the Poisson distribution with parameter . You toss each coin once, with heads showing with probability p each time. Show that the total number of heads has the Poisson distribution with parameter Ap.

Answer 1

Answerg pocket vandom number of No coins iS a poi eson distvibuton with panamctes N heads shouing with you tbss Each coin once, th probaity P Each time heads pith poisson Let k be the mumber distofbution wth parameter 2P - 2 ni, (a) N kf kIn) E (KIN) ph Thus E(kiN) Win) PN and -()1 PELN) = P2 E (k) ithas the poisson distibution So