mid01_sol _1_

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

This preview shows pages 1–2. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online