- #1
grimster
- 39
- 0
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)
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?
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?