mid01_sol _1_ - ISyE 2028A Summer 2010 1 Let 1,2,n be the...

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ISyE 2028A, Summer 2010 Friday June 4 Midterm 1 Solutions 1. Let 12 ˆˆ ˆ ,, , n θθ θ  be the maximum likelihood estimates (mle’s) of the parameters , n . Then the mle of any function h ( , n ) of these parameters is the function ˆ (, , , ) m h of the mle’s. This result is known as the __________ principle. [6 points] ANSWER: invariance 2. If Z is a standard normal random variable with cumulative distribution function () z Φ , then (1.65) ( 1.65) Φ −Φ − = __________. [6 points] ANSWER: .901 3. Which of the following is not a measure of variability? [6 points] A. Variance B. Standard deviation C. Mean absolute deviation D. Median E. All of the above ANSWER: D 4. If X has a normal distribution with mean µ and standard deviation σ , and Z is the standard normal random variable whose cumulative distribution function is ° ( ± ≤ ² ) = Φ ( ² ) , then which of the following statements are not correct? [6 points] A. ( )/ ZX µσ = B. ( ) [( )/ ] [ Pa X b b a = Φ C. ( ) 1 [( PX a a = −Φ D.
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mid01_sol _1_ - ISyE 2028A Summer 2010 1 Let 1,2,n be the...

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