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IE111_F09_Exam3a_solutions

# IE111_F09_Exam3a_solutions - IE 111 Fall 2009 9:00 Section...

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IE 111 Solutions Fall 2009 9:00 Section Exam 3 Instructions 1. The test is open book, open notes. 2. You must show sufficient work to receive credit. 3. You do not need to interpolate in any tables you use. Just use the closest value. 4. All probabilities should be worked out to a number when possible 5. Each of the 4 problems is worth 25%. 6. This test is long. Cumulative Poisson Distribution Tables lambda x 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 0 0.006 0.005 0.005 0.004 0.004 0.003 0.003 0.003 1 0.034 0.031 0.029 0.027 0.024 0.022 0.021 0.019 2 0.109 0.102 0.095 0.088 0.082 0.077 0.072 0.067 3 0.238 0.225 0.213 0.202 0.191 0.180 0.170 0.160 4 0.406 0.390 0.373 0.358 0.342 0.327 0.313 0.299 5 0.581 0.563 0.546 0.529 0.512 0.495 0.478 0.462 6 0.732 0.717 0.702 0.686 0.670 0.654 0.638 0.622 7 0.845 0.833 0.822 0.809 0.797 0.784 0.771 0.758 8 0.918 0.911 0.903 0.894 0.886 0.877 0.867 0.857 9 0.960 0.956 0.951 0.946 0.941 0.935 0.929 0.923 10 0.982 0.980 0.977 0.975 0.972 0.969 0.965 0.961 11 0.993 0.992 0.990 0.989 0.988 0.986 0.984 0.982 12 0.997 0.997 0.996 0.996 0.995 0.994 0.993 0.992 13 0.999 0.999 0.999 0.998 0.998 0.998 0.997 0.997 14 1.000 1.000 1.000 0.999 0.999 0.999 0.999 0.999 15 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 16 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 17 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 18 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

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Question 1 Random variable X has the following probability density function: f(x) = kx+k for -1 ≤ x ≤ 0 f(x) = -kx/3+k for 0 ≤ x ≤ 3 f(x) = 0 otherwise a) Find k so that f(x) is a valid pdf and graph the function.
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