Problem 5.5 (Video 4.1 - 4.5, Lecture Problem) You are manufacturing parts that have quite a bit of variability in their quality. Let us model this by saying X is Uniform[1,2]. The lifetime of a part is modeled by Y, and we know that Y given X = x is Exponential(x). (a) Are X and Y independent? (b) What is the joint PDF fx,y(x, y)? (c) Calculate P[Y < 1].

Problem 5.5 (Video 4.1 - 4.5, Lecture Problem) You are manufacturing parts that have quite a bit of variability in their quality. Let us model this by saying X is Uniform[1,2]. The lifetime of a part is modeled by Y, and we know that Y given X = x is Exponential(x). (a) Are X and Y independent? (b) What is the joint PDF fx,y(x, y)? (c) Calculate P[Y < 1].

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter2: Exponential, Logarithmic, And Trigonometric Functions

Section2.CR: Chapter 2 Review

Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...

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Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?