Question

Asked Aug 8, 2019

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Suppose that X_{i} ∼ Gamma(α_{i} , β) independently for i = 1, . . . , N. The mgf(moment generating function) of X_{i}is M_{Xi}(t) = (1 − (t/β) )^{−αi} . (a)Use the mgf of X_{i} to derive the mgf of ∑_{i=1} X_{i} .

Use the mgf of Xi to derive the mgf of ∑_{i=1} X_{i}

Step 1

**Introduction:**

It is given that *X _{i}*’s (

Step 2

**Derivation:**

The mgf of the sum of all *X _{i}*’s, that is, of Σ

Step 3

**Conclusion:**

The above derivation shows that Σ* Xi* has the Gamma (Σ* α...*

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