Expected heads from a biased coin

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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?

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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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