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8.2 The Geometric Distribution

Activity 8B. Instead of giving the normal 10 homework problems per night we will use probability to assign homework. I will select a student at random and then give the lucky student the opportunity to guess what day of the week, one of my many friends was born. If the chosen student guesses corre

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8.2 The Geometric Distribution

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    1. 8.2 The Geometric Distribution Objective 1) Describe what is meant by setting. Objective 2) Given the probability of success , p, calculate the probability of getting the first success on the nth trial. Objective 3) Calculate the mean (expected value) and the variance of a geometric random variable. Objective 4) Calculate the probability that it takes more than n trials to see the first success for a geometric random variable.

    2. Activity 8B Instead of giving the normal 10 homework problems per night we will use probability to assign homework. I will select a student at random and then give the lucky student the opportunity to guess what day of the week, one of my many friends was born. If the chosen student guesses correctly, I will assign only one homework problem. If he/she guesses wrong, he or she will try to guess the day on which another friend was born and if she gets it right I will assign two problems. We will continue this little game until the chosen one guesses correctly. The number of homework problems will be equal to the number of guesses. Is this a good plan?

    3. 1) Before you make a decision, try the birthday game for yourself. Play several times before you draw conclusions. 2) What is the theoretical probability that I assign exactly 10 homework problems this way. 3) Find the theoretical probability that I assign fewer than 10 homework problems. 4) Find the theoretical probability that I assign more than 10 homework problems.

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