Let X 1 , X 2 , …. X k be independent, binomially distributed random variables with respective parameters (n 1 , p 1 ), (n 2 , p 2 ), ...,(n k , p k ). Under which condition has the sum Z = X 1 + X 2...

Let X₁, X₂, …. X_k
be independent, binomially distributed random variables with respective parameters (n₁, p₁), (n₂, p²), ...,(n_k, p_k).

Under which condition has the sum Z = X₁
+ X₂
+ . .. + X_k
a binomial distribution? Hint Determine the z-transform of Z.