Show that a Binomial (n,p) random variable is a sum of n iid Bernoulli (p) random variables???

plz help wit dis...

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- Mar 30th 2010, 06:39 PMamul28Random variables
Show that a Binomial (n,p) random variable is a sum of n iid Bernoulli (p) random variables???

plz help wit dis... - Mar 30th 2010, 07:42 PMAnonymous1
Ok, on one condition... Never say "plz help wit dis..." again.

Bernoulli's have mass function $\displaystyle f(k;p) = p^k(1-p)^{1-k} $ for $\displaystyle k\in \{0,1\}.$

Now, Binomial has mass function $\displaystyle f(k;p) = {n\choose k} p^k(1-p)^{n-k}$ for $\displaystyle k=1,..,n$

i.e., $\displaystyle \sum_{k=0}^n {n\choose k} p^k(1-p)^{n-k} = (1-p)^{n} + {n\choose 1} p (1-p)^{n-1} + {n\choose 2} p^2 (1-p)^{n-2}+ ... $

What are you starting to see?

Wait I thought of an easier way to explain this... - Mar 30th 2010, 08:00 PMAnonymous1
Apply the Binomial theorem.

Sorry I just got really lazy. I've been doing straight math since 9am and have been posting here on my free time. Overdose. - Mar 30th 2010, 11:50 PMamul28
surely

thank u.....

ill try