Random Variables and their PDFs
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1) Swimming Medley (from DeVeaux & Velleman p 315 #37)
b) The team’s best time so far this season was 3:19.48 or 199.48 seconds. Do you think that the team is likely to swim faster than this at the conference championship? Explain.
2) A commuter airline flies planes between San Luis Obispo and San Francisco. For small planes, the baggage weight is a concern, particularly on foggy mornings, because weight has an effect on how quickly the plane can ascend. Suppose we know that the weight of baggage, checked by a random passenger has a mean and standard deviation of 42 and 16 pounds, respectively. Consider a flight on which ten passengers, all traveling alone, are flying.
b) If total baggage weight exceeds 500 pounds, there is cause for
concern. How likely will it be for the flight to be dangerously
These last few problems make use of the binomial distribution. However, they also illustrate some intuitive lessons about the law of large numbers. The law of large numbers says that sample average is more likely to be close to the expected value (a.k.a. the mean) for a large sample size than for a small sample size.
Sometimes Multiple Choice is a good teaching tool! Particularly if you add the "Explain."
3) A die will be rolled some number of times, and you win $1 if it shows an ace more than 20% of the time. Which is better? Circle one.
a) 60 rolls
4) A die will be rolled some number of times and you win $1 if the percentage of aces is exactly 16 and 2/3 %. Which is best? Circle one:
a) roll the die 60 times