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Let T1 and T2 be independent exponential random variables with a common mean 2. Find the...

Let T1 and T2 be independent exponential random variables with a common mean 2. Find the MGF and then identify the distribution of T1 + T2

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Answer #1

mgf of exponential distribution =1/(1-*t) where is mean of the exponential distribution

mgf of T1 M(T1) =1/(1-2*t)

mgf of T2 M(T2)=1/(1-2*t)

therefore mgf of T1+T2 =M(T1+T2) =M(T1)*M(T2) =(1/(1-2*t))*(1/(1-2*t)) =1/(1-2t)2

which is mgf of gamma distribution with parameter =2 and =2

therefore T1+T2 follows gamma distribution with parameter =2 and =2

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