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Unformatted text preview: 1 Solutions of Assignment #1  STAT 330 Due in class: Thursday May 19 Important Note: You need to print out this page as the cover page for your assignment. LAST NAME: FIRST NAME: ID. NO.: QUESTION 1. /12 QUESTION 2. /8 QUESTION 3. /3 QUESTION 4. /2 QUESTION 5. /9 QUESTION 6. /6 TOTAL: /40 2 1. Consider the following functions: (a). f ( x ) = k (0 . 3) x , x = 0 , 1 , 2 ,... (b). f ( x ) = kx 2 e λx , x > , λ > (c). f ( x ) = k (1 + x ) ( θ +1) , x > , θ > 0. In each case (i). Determine k so that f ( x ) is a pdf (or pmf) for a random variable X . (ii). Find the cdf F ( x ). (iii). Find E ( X ). 3 2. If X is Weibull distributed, X ∼ WEI ( θ,β ), with pdf f ( x ) = β θ β x β 1 exp n ( x/θ ) β o ,x ≥ ,β > ,θ > , find both the c.d.f. and p.d.f. of each of the following: a) Y = ( X/θ ) β b) W = ln( X ) c) Z = (ln X ) 2 4 3. Let X be a random variable having a t distribution with degrees of freedom n . Show that Y = X 2 follows an F distribution. Identify its degrees of freedom.distribution....
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 Spring '08
 PAULASMITH
 Statistics

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