Fall 2004
Practice Exam 2
Instructor: M. Kulenović
Kingston 10/10/2004
1. An exam given to a large number of students is scored from to The density function of the scores is shown in the figure below.
Estimate the percentage of students scoring between and
Estimate the percentage of students scoring less than
Estimate the median and the mean.
2. The density function for the lifetime for certain type of switching device is shown in the figure below. The time is measured in months and
Estimate the percentage of switching devices which lifetime is between and months
Estimate the percentage of switching devices which lifetime is less than months.
Estimate the mean and the median value of this switching device.
3. Given the following probability density function:
Find its cumulative distribution function.
Find its mean value and the median.
4. Match the graphs of surfaces to the equations. Explain.
(a) (b) (c)
(i) (ii)
(iii)
5. Match the contour diagrams to the equations in the previous problem. Explain.
(i) (ii)
(iii)
6. Fill in the blanks in a partial table of values for a linear function:
Find an equation for this linear function.
7. Consider the function
(a) Estimate and from a table of values for with and
(b) Compare the estimates in part (a) with the exact values of and
8. Suppose that your weight in pounds, is a function of the number of calories you consume daily and the height in inches. Using units, interpret, in everyday terms the statements:
(a) (b)
(c)
Estimate
9. Find all critical points of the function:
Determine if the critical points are local maxima, minima, saddle points, or none of these.
10. Design a rectangular milk carton box of width length and height which holds of milk. The sides of the box cost cent/ and the top and bottom cost cent/ Find the dimensions of a box that minimize the total cost of materials used.
11. Consider data points . Suppose you want to find a least square line for these data points without using a calculator program. What function should be minimized ?
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