We do so by means of a sequence of simulations in Excel. Now we analyze the distribution of winnings based on the average of n spins. So you are much less likely to win big if your winnings are based on the average of many spins.) If you play this game once and your winnings are based on the average of n spins, how likely is that you will win at least $600 if n = 1? if n = 3? if n = 10? (The answers are 0.4, 0.27, and 0.14, respectively, where the last two answers are approximate and are based on the central limit theorem or the simulation. ^5īefore we go any further, take a moment to test your own intuition. (See Figure 7.8, where the 1 on the horizontal axis corresponds to $1000.) It can be shown (with calculus) that the mean and standard deviation of this uniform distribution are μ = $500 and σ = $289. The resulting population distribution is called the uniform distribution on the interval from $0 to $1000. Furthermore, because we have assumed that the wheel is equally likely to land in any position, all possible values in the continuum from $0 to $1000 have the same chance of occurring. Each spin results in one randomly sampled dollar value from this population. First, what does this experiment have to do with random sampling? Here, the population is the set of all outcomes you could obtain from a single spin of the wheel-that is, all dollar values from $0 to $1000.
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