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recitation5 - to be high and a ﬁve-year return of in...

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Review and Examples Counting Outcomes of Experiments Assigning Probabilities Events Basic Probability Relationships Random Variables Discrete Probability Distributions Expected Value (Mean) Variance and Standard Deviation Suppose to win a lottery you must correctly match five numbers drawn from the numbers 1 through 40. How many ways could you select your five num- bers? What is the probability of winning this lottery by purchasing a single ticket? 1

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The following data show the five states with the largest number of Fortune 500 companies. Suppose a Fortune 500 company is selected for a questionnaire. State Number of Companies New York 54 California 52 Texas 48 Illinois 33 Ohio 30 a. Let N be the event that the company is headquartered in New York. Find P ( N ). Note that there are 500 total companies. b. Let B be the event that the company is headquartered in one of these five states. Find P ( B ). Data on the 30 largest stock and balanced funds provided one-year and five- year percentage returns. We will consider a one-year return in excess of 50%

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Unformatted text preview: to be high and a ﬁve-year return of in excess of 300% to be high. Nine of the funds had one-year returns in excess of 50%, seven of the funds had ﬁve-year returns in excess of 300%, and ﬁve of the funds had both one-year returns in excess of 50% and ﬁve-year returns in excess of 300%. a. What is the probability of a high one-year return? What is the proba-bility of a high ﬁve-year return? 2 b. What is the probability of both a high one-year return and a high ﬁve-year return? c. What is the probability of neither a high one-year return nor a high ﬁve-year return? The following table provides a probability distribution for the random vari-able x . x f ( x ) 3 .25 6 .50 9 .25 a. Make a graph of the probability distribution. b. Compute E ( x ), the expected value of x . 3 c. Compute σ 2 and σ , the variance and standard deviation of x . 4...
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