(1) Let X1 ~ B(n1, p). X2 ~ B(n2,p). By mgfs show that X1 + X2 ~ B(n1 + n2,p) when X1 , X2 are independent. The following "proofs" are provided. (a) The stated result is false. (b) The mgf of Z = Xı + X2 cqual to .(수). (수) n2 ni+n2 This is the mgf of B(n1 + n2,p). (6) The mgf of Z = X1 + X2 cqual to .(수) (1 – p + pe')" (1 – p + pe')": = (1 – p + pe')" +m² . This is the mgf of B(n1 + n2,p). d) The mgf of Z = X1 + X2 equal to This is the mgf of B(n1 + n2,p). te) None of the above.

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.