HW_13_14 - ECO220Y: Homework, Lectures 13 & 14...

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Page 1 of 1 ECO220Y: Homework, Lectures 13 & 14 Readings: Section 7.4 Exercises: 7.92, 7.94, 7.96, 7.97, 7.98 (Note: Solve these Exercises without a computer and without using any tables in the appendices) Problems: (1) What two factors affect the probability of any particular number of successes in a Binomial experiment? For example, what would affect the P(X = 1)? Make sure to explain the intuition. (2) Would the following be good examples of a Binomial random variable: number of hearts drawn in 5 draws with replacement from a standard 52 card deck; number of hearts drawn in 5 draws with out replacement from a standard 52 card deck? (3) For which (finite) number of tosses of a fair coin is the probability of getting exactly 50% heads the biggest? [Hint: Your answer should be of the form: n = #, where # is a number.] Explain and show work. (4) Consider doing a Binomial Experiment and defining a new random variable Y as the fraction of successes in the n trials. For example, if there are 3 successes in 5 trials, Y would be 0.60 whereas the Binomial random
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