(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose P(X_{n}= i) = [itex]\frac{n+i}{3n+6}[/itex], for i=1,2,3.

Find the limiting distribution of X_{n}

2. Relevant equations

3. The attempt at a solution

I first found the MGF by Expectation(e^{tx})

which resulted in e^{tx}([itex]\frac{n+1}{3n+6}[/itex] + [itex]\frac{n+2}{3n+6}[/itex] + [itex]\frac{n+3}{3n+6}[/itex])

I then took the limit as n[itex]\rightarrow[/itex] ∞ which gives me 2e^{tx}

Did I do this problem correctly? Is that the limiting distribution of Xn?

Thanks.

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# Limiting Distribution

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