What is the expected number of heads in n coin tosses, where the probability of landing one head is p?
I know that the probability of having k heads in n tosses is $$\ \binom{n}{k}p^k(1-p)^{n-k}$$
So, the expected number of heads in n tosses is $$\sum_{k=0}^n k\binom{n}{k}p^k(1-p)^{n-k}$$
But I'm not sure how to simplify this further. Any help would be appreciated!
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