quiz_2_fin_2005

# quiz_2_fin_2005 - Quiz 2 In-class open books and notes...

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Quiz # 2 In-class, open books and notes Problem 1 (40 Points) An environmental variable X has value X i in day i. Due to budgetary constraints, X is measured only every third day. If X is measured in day i, then the observed value of X i 1 is used to estimate the three-day average X = 3 (X i 1 + X i + X i + 1 ) . Given that the variables X i have multivariate normal distribution with common mean value m and common variance σ 2 and that the correlation coefficient between X i and X j is ρ ij = 0.9 |i j| , (a) Find the distribution of (X |X i ) . [Hint: start by finding the joint distribution of X and X i ]. (b) Based on the answer to (a), suggest a better estimator of X from X i . Problem 2 (30 Points) In a river reach, flooding occurs if the water level H exceeds 8 meters. Following a heavy rainstorm, the water level is H = H o + D I 5 . 0 8 . 0 , where H o is the water level before the storm, I is storm depth in meters/hour (integrated over the river catchment) and D is the

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quiz_2_fin_2005 - Quiz 2 In-class open books and notes...

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