PracticeQuestions3

# PracticeQuestions3 - Practice Questions 3 1 Which of the following is an example of a discrete random variable A B C D The distance you can drive

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Practice Questions 3 ECO 329 1. Which of the following is an example of a discrete random variable? A) The distance you can drive in a car with a full tank of gas. B) The number of cows on a cattle ranch. C) The weight of a package at the post office. D) The amount of rain that falls over a 24-hour period. 2. Which of the following is an example of a continuous random variable? A) The number of cars in a parking lot. B) The number of repairs at a computer shop over the course of the week. C) The total points scored in a basketball game. D) The weight of a bag of potatoes. 3. Consider the following probability distribution function. x 0 1 2 3 4 5 6 P ( x ) 0.07 0.19 0.23 0.17 0.16 0.14 0.04 a. What is P ( X > 3)? b. What is P (2 < X < 5)? c. What is P ( X r 2)? d. What is P ( X < 6)? 4. Consider the following probability distribution function. Compute the mean and standard deviation of x . x 0 1 2 3 4 5 6 7 P ( x ) 0.05 0.16 0.19 0.24 0.18 0.11 0.05 0.02 5. Suppose you know that the number of complaints coming into a phone center averages 4.2 every ten minutes. Assume that the number of calls follows the Poisson distribution. What is the probability that there are exactly three calls during the next ten minutes?

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6. An auditor reviewing the invoices of a small company finds that there are errors in 1.5% of them. If the auditor looks at 500 invoices, what is the probability that he finds more than 3 invoices with errors? 7. The following table displays the joint probability distribution of X and Y . What is the covariance between the X and Y ? X 1 2 3 1 0.10 0.08 0.06 Y 2 0.16 0.1 0.11 3 0.02 0.16 0.21 8. The following table displays the joint probability distribution of two discrete random variables X and Y . What is the covariance between X and Y ? X 1 2 3 0 0.10 0.12 0.06 Y 1 0.05 0.10 0.11 2 0.02 0.16 0.28 a. Determine the marginal probability distribution for X . b. Compute the expected value for X . c. Compute the standard deviation for X . d. Determine the marginal probability distribution for Y . e. Compute the expected value for Y . f. Compute the standard deviation for Y . g. Compute the covariance between X and Y .
h. Compute the correlation between X and Y . i. Compute the mean for the linear function W =2 X + Y . j. Compute the variance for the linear function W = 2 X + Y . k. Are X and Y statistically independent? Explain. 9. Consider the following probability distribution function for questions 3 and 4. x

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## This note was uploaded on 04/13/2008 for the course ECON 329 taught by Professor Yilmaz during the Spring '08 term at University of Texas at Austin.

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PracticeQuestions3 - Practice Questions 3 1 Which of the following is an example of a discrete random variable A B C D The distance you can drive

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