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Unformatted text preview: EAS 305 Applied Probability & Statistics Inference Homework 3 Due Day: September 29, 2010 (in Class) 1. A car rental agency has either 0 , 1 , 2 , 3 , 4 , or 5 cars returned each day, which probabilities 1 6 , 1 6 , 1 3 , 1 12 , 1 6 and 1 12 , respectively. Find the mean and the variance of the number of cars returned. 2. The cumulative distribution function that a television tube will fail in t hours is 1- e- ct , where c is a parameter dependent on the manufacturer and t ≥ 0. Find the probability density function of T , the life of the tube. 3. Consider the three functions given below. Determine and explain which functions are distribution functions (CDFs). (a) F X ( x ) = 1- e- x , < x < ∞ . (b) G X ( x ) = ( e- x , ≤ x < ∞ , , x < . (c) H X ( x ) = ( e x ,-∞ < x ≤ , 1 , x > . 4. Refer to problem 3 mentioned above. Find the probability density function corresponding to the function given, if they are distribution functions....
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This note was uploaded on 10/31/2010 for the course EE 423 taught by Professor Mitin during the Spring '10 term at SUNY Buffalo.
- Spring '10