Question

Use R - stuido

6. Consider a fair coin. If Y = # of tosses until first H, what are P(success), EY, and VY?

7. Next, take a quarter and record # of tosses until first H. Do this experiment 30 times: so that your first experiment consists of your tosses up to your first H, and you record the number of T before the coin came up heads. Then you pretend to start over: reset your count and toss the coin until you get a H again. The count of T before the second H but after the first H will be the value y for your second experiment. Continue to do this until you have 30 values y for Y. Record this data in R using c().

8. Plot a histogram of these 30 values.

9. In R, calculate the average and sample variance of the 30 values you recorded. Is it close to the expected value and variance of Y?

10. Next take a penny and repeat Q7.

11. Plot a comparative boxplot of your quarter data and penny data. Are they similar or different?

12. In R, calculate the average and sample variance of the 30 values you recorded for the penny data. Is it close to the expected value and variance of Y?

13. If either of the above coins do not seem similar to EY and VY, consider: if the P(H) ≠ .5 of a coin, how might Ex and Vx change? To answer this, consider what happens to EY when P(H) > .5 and when P(H) < .5. For VY, try to draw a graph of P(H) versus VY 1. Learn about binomial and geometric r.v.s by conducting experiments and collecting data 2. Address binomial and geometric problems through different angles a. finding parameters versus verifying probabilities or b. identifying situations to fit models versus creating situations to fit models using the R function plot(, ), where should be a sequence of values using seq(from=, to = , by = .1) and describe the trends of the graph.

Answer 1

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