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["LLN For Binomial Random Variable"]
[]
[]
["Number of trials",10,null,"  Enter data in yellow cells."]
["Probability of a success",0.7,null,"  Enter function formula in B9."]
["Number of runs",10000,null,"  Outputs appear in B11 and B12."]
[]
["k (no. of heads)"]
["f(k)",{"$f":"B8^2","v":0},null,null,null,null,"        Illustrates the law of averages for iid random variables of the form f(X),"]
[null,null,null,null,null,null,"  where X is a binomial random variable with parameters given in B4 and B5 and"]
["Sample average",51.115299999999998,null,null,null,null,"  f is a user defined or Excel function entered in cell B9 with argument in B8"]
["Expectation",51.099998378753668,null,null,null,null,"  (for example, = B8^3, or = SIN(B8)). Sample averages are gotten by performing"]
[null,null,null,null,null,null,"  the number of runs in B6, each run consisting of the number of trials given in B4."]
[null,null,null,null,null,null,"  Each trial may be viewed as a coin toss (simulated by a random number generator). "]
[null,null,null,null,null,null,"  The results of the runs are averaged and placed in B11. The expectation of the"]
[null,null,null,null,null,null,"  random variable f(X) is given in B12 for comparison."]

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