i have X_1,X_2,...X_n independant poisson-distributed variables with parameters: alfa_i and i=1,...k(unsure about this. however says so in the excercise)(adsbygoogle = window.adsbygoogle || []).push({});

i am supposed to find the distribution of

Y= SUM(from 1 to n) a_i*X_i where a_i>0

maybe one could use the "poisson paradigm" by thinking of each variable as a trial with p_i as the chance for success. so that

E[e^tX_i]=1+p_i(e^t - 1)

and

E[e^tX] is approximately

(product from i=1 to n) EXP{p_i(e^t - 1)

the problem is the a_i part. how do i find the mfg of Y?

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# Homework Help: Finding distribution by using mgf(moment generating function)

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