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Simulating Experiments

This introduction to simulating experiments explains the steps involved in accurately reflecting experimental outcomes using models. Learn to state the problem, define key components, select a model, conduct trials, record observations, and draw conclusions with examples of tossing a coin and shooting free throws.

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Simulating Experiments

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  1. Simulating Experiments • Introduction to Random Variable

  2. Simulation The imitation of chance behavior based on a model to accurately reflects the experiment under consideration

  3. Steps in simulating experiments: • State the problem clearly • Define the key components • State the underlying assumptions • Select a model to generate the outcomes for a key components • Define and conduct a trial • Record the observation of interest • Repeats steps 5 and 6 at a large number of times • Summarize the information and draw conclusions

  4. Example: A run of three in tossing a coin 10x Step 1 State the problem: Toss a coin 10 times. What is the likelihood of a run of at least 3 consecutive heads or 3 consecutive tails Step 2 State the assumption: There are 2. 1. A head or a tail is equally likely to occur 2. Tosses are independent of each other. (what happens on the first toss will not influence the next toss) Step 3 Assign digits to represent outcomes Using random number table on Table B we assign: 1. One digit simulate one toss of the coin 2. Odd represents heads, even digits represents tails

  5. Step 4 Simulate many repetition: looking at 10 consecutive digits on table B, simulate one repetition. Read as many groups of 10 from the table to simulate many repetitions: Let’s use line 101 of table B for our first three rounds of simulation. 22 more rounds were added and out of the 25 rounds. 23 of them did have a run of three Yes First round: Yes 2nd round: Yes 3rd round:

  6. Step 5 State your Conclusion: We estimate the probability of a run of size 3 by the proportion Estimated probability= 23/25= 0.92 There is a 92% chance of getting a run of three when you toss a coin 10 times. True mean: 0.826

  7. Difference between dependent and independent trial Independent trial: the number of trials has no effect on the succeeding trial Example: tossing a die, flipping a coin, drawing a card Dependent trial: shooting 10 free throws in a basketball. Getting an A on the first quiz.

  8. Shooting free throws Lisa makes 70% of her free throws in a long season. In a tournament game she shoots 5 free throws late in the game and misses 3 of them. The fans think she was nervous, but the misses may simply be chance. You will shed some light by estimating a probability.

  9. answer Shooting Free Throws: Single random digit will simulate a shot, with 0-6 representing the basket made and 7,8,9 representing the miss. 5 consecutive digits using Table 5 can simulate 5 shots. After 46 more repetitions: The relative frequency of missing three or more shots in five attempts is 11/50= 0.22

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