A certain manufacturing process creates pieces of pasta that vary by length. Suppose that the length...
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A certain manufacturing process creates pieces of pasta that vary by length. Suppose that the length of a particular piece (represented as a random variable L that takes on values /), is a continuous random variable with the following probability density function. (0, f(1) = {c.l, 0<I<2, 0, 2</ where e is a constant that makes f(1) a valid probability distribution function. a. (3 points) Compute the constant c. What value of e makes f(1) a valid pdf? b. (1 point) What is the cumulative probability when I< 0? c. (1 point) What is the cumulative probability function when 0 <IS 2? d. (1 point) What is the cumulative probability function when 2 < 1? e. (3 points) Compute the median value of L. That is, compute / such that P(L <1) = 1/2. A certain manufacturing process creates pieces of pasta that vary by length. Suppose that the length of a particular piece (represented as a random variable L that takes on values /), is a continuous random variable with the following probability density function. (0, f(1) = {c.l, 0<I<2, 0, 2</ where e is a constant that makes f(1) a valid probability distribution function. a. (3 points) Compute the constant c. What value of e makes f(1) a valid pdf? b. (1 point) What is the cumulative probability when I< 0? c. (1 point) What is the cumulative probability function when 0 <IS 2? d. (1 point) What is the cumulative probability function when 2 < 1? e. (3 points) Compute the median value of L. That is, compute / such that P(L <1) = 1/2.
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Related Book For
Probability and Statistics
ISBN: 978-0321500465
4th edition
Authors: Morris H. DeGroot, Mark J. Schervish
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