# HW3 - EAS 305 Applied Probability Statistics Inference...

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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 , 0 < x < . (b) G X ( x ) = ( e - x , 0 x < , 0 , x < 0 . (c) H X ( x ) = ( e x , -∞ < x 0 , 1 , x > 0 . 4. Refer to problem 3 mentioned above. Find the probability density function corresponding to the function given, if they are distribution functions. 5. The demand for a product is - 1, 0, +1, +2 per day with probabilities 1 5 , 1 10 , 2 5 , 3 10 , respectively. A demand of - 1 implies a unit is returned. Find the expected demand and the variance. Sketch the

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