Math Help - Random variables

1. Random variables

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

2. 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...

3. 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.

4. surely
thank u.....
ill try