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Unformatted text preview: Stat315 Applied Probability and Statistics Midterm 2 (Fall 2009) Name: Score: Students are required to finish the exam in class within two hours independently. Cheating is NOT allowed. Any forms of cheating or attempt to cheat is a serious offense which may lead to dismissal! Calculators (including TIcalculators) and two formula sheets are allowed. Please follow the steps to perform a test of hypothesis with either the critical value approach or the pvalue approach. 1. Let f XY ( x,y ) = kxy for x = 1 , 3 and y = 1 , 2 be the joint probability function for discrete random variables X and Y . (a) Determine the value of k . (b) Compute P ( X = 1). (c) Compute E ( XY 2 ). 1 2. X and Y are independent, normal random variables with E ( X ) = 1, V ( X ) = 4, E ( Y ) = 10, and V ( Y ) = 9. Determine (a) E (2 X + 3 Y ). (b) V (2 X + 3 Y ). (c) P (2 X + 3 Y > 40). 2 3. Suppose that samples of size n = 25 are selected at random from a normal population with mean 100 and standard deviation 10. What is the probability that the sample mean falls in the interval from μ ¯ X 1 . 5 σ ¯ X to μ ¯ X + 2 . σ ¯ X ?...
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 Fall '11
 Staff
 Normal Distribution, Standard Deviation, Variance, Probability theory, probability density function

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