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Unformatted text preview: Question 7: Consider f X ( x ) and f Y ( y ) as follows. f X ( x ) = ( ex if x ≥ otherwise f Y ( y ) = 0 . 5 e y  Compute the following two integrals Z ∞ y =∞ Z ∞ x =∞ ( x + y ) f X ( x ) f Y ( y ) dxdy Z ∞ y =∞ Z ∞ x =∞ e. 1( x + y ) f X ( x ) f Y ( y ) dxdy Question 8: Problem 2.28. Answer the following questions ﬁrst. 1. What is the sample space? 2. What is the corresponding weight assignment? Hint: It is a continuous sample space so you have to use a curve f X ( x ) to describe your weight assignment Question 9: (It is actually Problem 2.30.) For any valid weight assignment over a continuous sample space, answer the following questions. 1. Show that we must have P ( X ∈ (∞ ,r ]) ≤ P ( X ∈ (∞ ,s ]) if r < s . 2. Suppose we know the values of P ( X ∈ (∞ ,r ]) and P ( X ∈ (∞ ,s ]). What is the value of P ( X ∈ ( r,s ]). Question 10: Problem 2.51....
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 Spring '08
 GELFAND
 Englishlanguage films, [email protected], Kamesh Krishnamurthy

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