practiceset44

3. Let X be a random variable that is uniform on [3 , 6]. a. If we make a box with area Y = ( X - 1)( X + 1), what is the CDF of Y ? [Hint: Note that (2)(4) ≤ Y ≤ (5)(7), i.e., 8 ≤ Y ≤ 35.] b. What is the density f Y ( y ) of the area Y of the box? c. Use the density of Y to get the expected area by integrating, i.e., E ( Y ) = R 35 8 y f Y ( y ) dy . d. Check your answer: Integrate with respect X to get the same expected area, i.e., E (( X - 1)( X + 1)) = R 6 3 ( x - 1)( x + 1) f X ( x ) dx . 3