Expected heads from a biased coin

Question

A biased coin lands heads with probability 0.3 on each flip. You flip it 20 times. On average, how many heads will you get?

Accepted Answer

Write the total number of heads as a sum of 20 indicators, one per flip, where each indicator is 1 if that flip is a head. Each flip is a head with probability 0.3, so by linearity of expectation the expected total is the sum of those individual probabilities: E[	ext{heads}] = 20 	imes 0.3 = 6. There is no need to worry about the spread of outcomes or any binomial formula. The average count of a repeated event is just the number of trials times the per-trial probability. Takeaway. The expected number of successes in n independent trials, each with success probability p, is simply np. Here 2…

Expected heads from a biased coin

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