Use the moment-generating function technique to rework Exercise 7.27. In exercise If X1 and X2 are independent

Question:

Use the moment-generating function technique to rework Exercise 7.27.
In exercise
If X1 and X2 are independent random variables having binomial distributions with the respective parameters n1 and θ and n2 and θ, show that Y = X1 + X2 has the binomial with the parameters n1 + n2 and θ.
Distribution
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