Need help figuring out the 2 questions attached in the image.

Thank you in advance!!

let X 1 .. . xm be iid Poisson ( d.) and Y .... you be iid boisson ( 12 ) and independent of X 1,. .. X m . S, = E x, and S , = s y ; are independent Poissons with parameters my , and n12 . a) show that the conditional distribution of S given that ( S , + s, = 8 ) is binomial with parameters ( s p ) where b) Test the null hypothesis H.: 0 2 1 versus H.: 0