(i) If X - N(u1, oi) and Y ~ (2 02), then X +Y - N(H1 + H2 oi + o). Gð If X is binomially distributed with parameters n1 and p and Y is binomially distributed with parameters n2 and p, then X+ Y is also binomially distributed with parameters n1 + n2 and p. i) If X is Poisson distributed with parameter u1 and Y is Poisson distributed with parameter uz then X+ Y is Poisson distributed with parameter µ1 + µ2.

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Theorem 6.1.5 Let X and Y be independent random variables. Then
(i) If X ~ N(H1, of) and Y ~ N(H2 o3), then
X +Y - N(u1 + H2 of + o2).
) If X is binomially distributed with parameters nj and p and Y is
binomially distributed with parameters n2 and p, then X+Y is
also binomially distributed with parameters n1 + n2 and p.
Gii) If X is Poisson distributed with parameter µ1 and Y is Poisson
distributed with parameter uz then X+ Y is Poisson distributed
with parameter µ1 + µ2.
Transcribed Image Text:Theorem 6.1.5 Let X and Y be independent random variables. Then (i) If X ~ N(H1, of) and Y ~ N(H2 o3), then X +Y - N(u1 + H2 of + o2). ) If X is binomially distributed with parameters nj and p and Y is binomially distributed with parameters n2 and p, then X+Y is also binomially distributed with parameters n1 + n2 and p. Gii) If X is Poisson distributed with parameter µ1 and Y is Poisson distributed with parameter uz then X+ Y is Poisson distributed with parameter µ1 + µ2.
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