Show that a Binomial (n,p) random variable is a sum of n iid Bernoulli (p) random variables???
plz help wit dis...
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...