This
preview
has intentionally blurred sections.
Sign up to view the full version.
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....
View
Full Document
- Spring '08
- GELFAND
- English-language films, [email protected], Kamesh Krishnamurthy
-
Click to edit the document details