In this experiment we test the Law of Large Numbers which states that “as an exp

Question

In this experiment we test the Law of Large Numbers which states that “as an experiment is repeated again and again, the empirical probability of success tends to approach the actual probability.” We will use a simulation of a single die, and we will consider a success to be the outcome of a 1. (Based on the classical definition of probability, we know that P(1) = 1/6 = 0.167.)

Simulate 50 trials in StatCrunch (Discrete Uniform) by generating 50 integers between 1 and 6. Count the number of ones that occurred and divide that number by 50 to get the empirical probability.

Based on 50 trials, P(1)

Repeat part (a) for 100 trials. Based on 100 trials, P(1)

Repeat part (a) for 500 trials. Based on 500 trials, P(1)

Repeat part (a) for 5,000 trials. Based on 5,000 trials, P(1)

Repeat part (a) for 10,000 trials. Based on 10,000 trials, P(1)

Based on parts a-e, do your results support the law of large numbers? Explain why or why not:

Explanation / Answer

Based on 50 trials, P(1) 0.15

Repeat part (a) for 100 trials. Based on 100 trials, P(1) 0.16

Repeat part (a) for 500 trials. Based on 500 trials, P(1) 0.174

Repeat part (a) for 5,000 trials. Based on 5,000 trials, P(1) 0.1588

Repeat part (a) for 10,000 trials. Based on 10,000 trials, P(1) 0.1635

As sample size increase the probability value reach to actual value i.e. 1/6 = 0.1666

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