hmwk8 - ISyE 2027 R. D. Foley Probability with Applications...

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ISyE 2027 Probability with Applications Fall 2006 R. D. Foley Homework 8 November 9, 2006 due on Tuesday 1. Suppose X is a continuous random variable with probability density function f ( s ) = cs 2 for 0 s 1. Compute the following: (a) c , (b) Pr { X 2 / 3 } , (c) Pr { X > 2 / 3 } , (d) Pr { X = 2 / 3 } , (e) Pr { X 1 / 3 | X 2 / 3 } , (f) Pr { X 2 / 3 | X 1 / 3 } , Pr { X 3 } , and Pr { X ≤ - 4 } . 2. For the previous problem, see if you can determine some function F ( t ) so that F ( t ) = Pr { X t } for -∞ < t < . 3. Suppose Y is a continuous random variable with p.d.f. c | s | for - 1 s 1. Determine c . 4. At the beginning of the course, we talked about the angle formed by the valve stem on the right front time of particular student’s car. Let U be the angle. Assume that if the valve was at the very front of the tire, then U = 0. If the valve were at the top of the tire, then U = π/ 2. What would be a reasonable choice for the p.d.f. of
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