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# exam2-421 - STT 421 Summer 2008 Exam#2 Instructor Erkan...

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STT 421 Summer 2008 Exam #2 Instructor: Erkan Nane Name: PID: Instructions Read each problem carefully. Show all your work. Credit will only be awarded if your work is included. Each part in a question worths the same! Problem max-points Points 1 15 2 15 3 10 4 15 5 20 6 5 7 5 8 20 9 15 10-bonus 20 Total 140 1

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Problem 1. You purchase a stock for \$1000. The stock gains 20% or loses 10% each day, each with a probability 0 . 5. Its returns on consecutive days are independent of each other. You plan to sell the stock after two days. a. Find the distribution of the values of the stock after two days (in other words, what are the possible values of the stock after two days, and what is the probability of each value?) Give it in the form of a table. b. What is the probability that the stock is worth more after two days than the \$1000 you paid for it? c. What is the mean value of the stock after two days? 2
Problem 2. Suppose that 20% of the population has Type A blood. If a random sample of 81 people is selected, what is the approximate probability that 15 or fewer people in the sample have Type A blood? a. What is explicitly the random varable X having a Binomial distribution? b. Use the Normal approximation with continuity correction to find the desired probability, use X N np, np (1 - p ) . Problem 3. A researcher makes a measurement in a biology laboratory and records the result in his laboratory report. The standard deviation of his lab measurements is σ = 10 miligrams. The researcher repeats the measurement

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