Let the independent random variables X1 and X2 have binomial distributions with parameters n1, p1 =...

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Let the independent random variables X1 and X2 have binomial distributions with parameters n1, p1 =...

Let the independent random variables X1 and X2 have binomial distributions with parameters n1, p1 = 1/2 and n2, p2 = 1/2 , respectively. Show that Y = X1−X2+n2 has a binomial distribution with parameters n = n1+n2, p = ½

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Answer 1

Answer #1

Given that the independent random variables and have binomial distributions with parameters and , respectively. Since , has the same distribution as since since .

Note the PMF of is . Now we prove the sum of 2 binomial random variables

and with parameters and has Binomial distribution.

That is . Thus we have proved that

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Answer 2

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