Let X1,X2,X3 and X4 be independent random variables. Assume that X2,X3 and X4 each are poison distributed with mean 5, suppose Y=X1+X2+X3+X4~ POI(25). What is the distribution of X1. Solution pendent random variables. Assume that X2,X3 and X4 each are poison distributed with mean 5, suppose Y=X1+X2+X3+X4~ POI(25). What is the distribution of X1. Y will be poissone with mean of 5 + 5 + 5 + X1 so 5 + 5 +5 + x1 = 25 ( but given is 25) x1 = 25 - 15 x1 = 10 X1 is poison random with mean = 10.