An Extremely Biased Coin - II

Let $X$ be the number of heads obtained after tossing the coin 100 times. Then $X$ has a binomial distribution. That is, if there were $n$ Bernoulli trials, with the probability of success being $p$ , then the probability of $r$ successes is given by:

$P( X = r ) = \binom { n } { r } \ p ^{ r } ( 1 - p)^{ n - r }$

The expected value of $X$ in a binomial distribution is given by $n p$ . In the problem, there are $100$ trials: $n = 100$ , and the probability of success is $p = \frac{ 99 } { 100 }$ .

Therefore the expected value of $X$ is $E( X ) = 100 \times \frac{ 99 } { 100 } = \boxed{ 99 }$ $_\square$

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To see the proof that $E( X) = np$ , click here