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206F07_Lab7(2) - Math 206 Lab 7 1 Condence Interval For The...

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Math 206 - Lab 7 1 Confidence Interval For μ The coupon collector problem is a famous probability problem dealing with a contest where each time you buy something, you are giving a coupon, one of a set. Once you collect the entire set, you win a prize. However, each time you buy the product, you are given one of the coupons at random, each as likely as the next. If there are k total coupons, the least number of purchases you can make and win the prize is k , though for large k , this is probably unlikely. Something with the identical probabilistic behavior is the experiment where you roll a die until you have observed all 6 sides, thus k = 6. a. Calculate the probability that you observe all 6 sides in your first 6 rolls. (Think about the events ‘The resulting side has yet to be observed’). b. What do you think is the average number of rolls needed to have observed all 6 sides? Write this number down. c. Go to the website http://www-stat.stanford.edu/~susan/surprise/Collector.html and simulate 15 games. Record the resulting number of rolls in each experiment
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