Random variables

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March 30th 2010, 06:39 PM
amul28

Random variables

Show that a Binomial (n,p) random variable is a sum of n iid Bernoulli (p) random variables???
plz help wit dis...
March 30th 2010, 07:42 PM
Anonymous1

Ok, on one condition... Never say "plz help wit dis..." again.

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

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

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

What are you starting to see?

Wait I thought of an easier way to explain this...
March 30th 2010, 08:00 PM
Anonymous1

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.
March 30th 2010, 11:50 PM
amul28

surely
thank u.....
ill try

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