Let S be the number of heads in 1,000,000 tosses of a fair coin. How does on use (a) Chebyshev's inequality and (b) the Central Limit Theorem to estimate the probability that S lies between 499,500 and 500,500?
Thanks so much!!!
Let S be the number of heads in 1,000,000 tosses of a fair coin. How does on use (a) Chebyshev's inequality and (b) the Central Limit Theorem to estimate the probability that S lies between 499,500 and 500,500?
Thanks so much!!!
n=1,000,000 and p=.5 approximating this binomial with a normal (CLT) you need
and
Since you want the probability of an event that has at its center this is straightforward.
As for cheby's figure out your k at http://en.wikipedia.org/wiki/Chebyshev's_inequality
look under Probabilistic statement