6. (15 pts.) Here's a dataset I just generated. I'm not going to tell you what...

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6. (15 pts.) Here's a dataset I just generated. I'm not going to tell you what distribution I generated the data from because......I don't want to. 1.491, 0.019, 0.318, 0.056, 0.816, 0.978, 0.174, 0.461, 0.495, 0.547, 0.123, 2.270, 0.026, 0.041, 0.391 1 (a) Use the bootstrap method to estimate the probability that a random variable coming from this distribution is less than 0.75. Give a 95% confidence interval of your estimate. (b) Do you think the bootstrap method is a good way to estimate such a number? Defend your answer with a simulation study. Let me be more specific: generate random numbers from a distribution in which you know what the probability of being less than 0.75 is. Then implement the bootstrap and see how close you get to the probability you know. 6. (15 pts.) Here's a dataset I just generated. I'm not going to tell you what distribution I generated the data from because......I don't want to. 1.491, 0.019, 0.318, 0.056, 0.816, 0.978, 0.174, 0.461, 0.495, 0.547, 0.123, 2.270, 0.026, 0.041, 0.391 1 (a) Use the bootstrap method to estimate the probability that a random variable coming from this distribution is less than 0.75. Give a 95% confidence interval of your estimate. (b) Do you think the bootstrap method is a good way to estimate such a number? Defend your answer with a simulation study. Let me be more specific: generate random numbers from a distribution in which you know what the probability of being less than 0.75 is. Then implement the bootstrap and see how close you get to the probability you know.