If moment generating function is $m(t)=[(1/3)e^{t}+(2/3)]^{5}$,
then what is the distributions of the random variable?
2026-05-06 07:37:18.1778053038
what is the distributions of the random variable?
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Maybe work backwards. The mgf of a sum of independent random variables is the product of the mgf. So our mgf is the mgf of a sum $X_1+X_2+\cdots +X_5$ of $5$ independent random variables with mgf $(1/3)e^t +2/3$. Now do we recognize this? Hint: What is the mgf of a random variable which is $1$ with probability $p$ and $0$ with probability $1-p$?