4.4 The Absolute Excess of Heads over Tails
distributionXwith a parameter 1/100 which implies thatE[X] = 100
and Var [X] = 100^2. The company can afford some overstatements sim-
ply because it is cheaper to pay than it is to investigate and counter-
claim to recover the overstatement. Given 100 claims in a month, the
company wants to know what amount of reserve will give 95% cer-
tainty that the overstatements do not exceed the reserve. (All units
are in dollars.) What assumptions are you using?Outside Readings and Links:
- Virtual Laboratories in Probability and Statistics. Search the page for
Binomial approximation and then run the Binomial Timeline Experi-
ment. - Central Limit Theorem explanation Pretty good visual explanation of
the application of the Central Limit Theorem to sampling means. - Central Limit Theorem explanation Another lecture demonstration of
the application of the Central Limit Theorem to sampling means.
4.4 The Absolute Excess of Heads over Tails
Rating
Mathematically Mature: may contain mathematics beyond calculus with
proofs.
Section Starter Question
What does the law of averages have to say about the probability of having a
fixed lead of say 20 Heads or more over Tails or 20 Tails or more over Heads
at the end of a coin flipping game of some fixed duration? What does the
Weak Law of Large Numbers have to say about having a fixed lead? What
does the Weak Law have to say about having a proportional lead, say 1%?
What does the Central Limit Theorem have to say about the lead?