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Assignment3

# Assignment3 - 1 Assignment#3 STAT 330 Due in class Thursday...

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1 Assignment #3 - STAT 330 Due in class: Thursday Mar. 25 Important Note: You need to print out this page as the cover page for your assignment. LAST NAME: FIRST NAME: ID. NO.: QUESTION 1. /5 QUESTION 2. /5 QUESTION 3. /6 QUESTION 4. /6 QUESTION 5. /6 QUESTION 6. /7 TOTAL: /35

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2 1. Suppose X UNIF [0 , 1] ,Y [0 , 1] , and X and Y are independent. Let U =( - 2 log X ) 1 / 2 cos(2 πY ) V - 2 log X ) 1 / 2 sin(2 ) Find (a). the joint p.d.f of U and V (b). the marginal p.d.f’s of U and V
3 2. Suppose that X and Y are independent r.v.’s, each with a N (0 , 1) distribution. Using the c.d.f method, Fnd the p.d.f of U = X + Y .

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4 3. Suppose that X i N ( μ,σ 2 ) ,i =1 , 2 ,...,n , and Z i N (0 , 1) , 2 ,...,m , and all random variables are independent. Let ¯ X = 1 n n i =1 X i and ¯ Z = 1 m m i =1 Z i . Use the results we discussed in class, identify the name of the distribution for each of the following random variables. Explain. (a). Z 2 1 + Z 2 2 (b). Z 2 1 Z 2 2 (c). X 1 - X 2 σ 2 q 1 m - 1 P m i =1 ( Z i - ¯ Z ) 2 (d). mn ( ¯ X - μ ) σ P m i =1 Z 2 i (e). 1 σ 2 n i =1 ( X i - μ ) 2 + m i =1 ( Z i - ¯

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Assignment3 - 1 Assignment#3 STAT 330 Due in class Thursday...

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