sample midterm

# Probability and Statistics for Engineering and the Sciences (with CD-ROM and InfoTrac )

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Midterm Examination, Statistics 220, Fall 2005 19 October 2005 Name: You have 50 minutes. You can use your own cheat-sheet and your own calculator. Please don’t share anything. Show your work. Ask us if you need extra scratch-paper. Exercise 1 /10 Exercise 2 /5 Exercise 3 /5 Exercise 4 /10 Problem 5 /20 Problem 6 /20 Problem 7 /30 Total /100 1

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1 Binomial vs. Poisson X is a binomial random variable, n = 10, p = 0 . 1. Y is a Poisson random variable, λ = 1. (a) What is E [ X ]? (1 pt) What is Var ( X )? (1 pt) What is the probability that X = 2? (3 pts) (b) What is E [ Y ]? (1 pt) What is Var ( Y )? (1 pt) What is the probability that Y = 2? (5 pts) 2
2 Camels Bactrian camels ( Camelus bactrianus ) are used as beasts of burden in Central Asia. A survey of the camels available in a certain town in Afghanistan shows that their mean weight is 1600 pounds, with a standard deviation of 150 pounds. (a) What are the mean and standard deviation of the camels’ weights in kilograms? (2 pts) Hint : 1 kg = 2.2 lb. (b) The camels are now loaded with water casks weighing exactly 120 kilograms each. What is the mean and standard deviation of their total weight? (3 pts) 3

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3 Coins (a) What are the probabilities of getting the following sequences of heads and tails from 10 consecutive tosses of a fair coin? (2 pts) (i) HHHHHHHHHH (ii) HTHTHTHTHT (iii) HHTTTTTTHH (b) What is the probability of getting 0 heads in 10 consecutive tosses? 5 headsout of 10? 6 out of 10? (3 pts) 4
4 Dice A fair die is one where all six faces are equally likely. (a) Let X = the number that comes up on a fair die. What is E [ X ]? (5 pts) (b) Let X 1 , X 2 and X 3 be three independent fair die, and S = X 1 + X 2 + X 3 . What is E [ S ]? (2 pts) (c) What is Pr ( S = 18)? (3 pts) 5

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5 A Continuous Random Variable Consider a continuous random variable X which lies between - 1 and +1. The density of X
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## sample midterm - Midterm Examination, Statistics 220, Fall...

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