In Exercise 5.6, we assumed that if a radioactive particle is randomly located in a square with sides of unit length, a reasonable model for the joint density function for Y1 and Y2 is f (y1, y2) = $ 1, 0 y1 1, 0 y2 1, 0, elsewhere. a Find the marginal density functions for Y1 and Y2. b What is P(.3 < Y1 < .5)? P(.3 < Y2 < .5)? c For what values of y2 is the conditional density f (y1|y2) defined? d For any y2, 0 y2 1 what is the conditional density function of Y1 given that Y2 = y2? e Find P(.3 < Y1 < .5|Y2 = .3). f Find P(.3 < Y1 < .5|Y2 = .5). g Compare the answers that you obtained in parts (a), (d), and (e). For any y2, 0 y2 1 how does P(.3 < Y1 < .5) compare to P(.3 < Y1 < .5|Y2 = y2)?

Chapter 11 --- Means (Sampling Distribution, Confidence Intervals, Hypothesis Tests) Sampling Distribution of a Sample Mean Example 1: The Arm and Hammer Company wants to ensure that their laundry detergent actually contains 100 fluid ounces, as indicated on the label. Historical summaries from the filling process indicate the mean amount per container is 100 fluid ounces and the standard...