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Unformatted text preview: Question 7: Consider f X ( x ) and f Y ( y ) as follows. f X ( x ) = ( e-x 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 contin-uous 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
- English-language films, [email protected], Kamesh Krishnamurthy