HW3 - STAT113 HW3 For Quiz 09/18/09 1. ( Chapter 4: 100 )...

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Unformatted text preview: STAT113 HW3 For Quiz 09/18/09 1. ( Chapter 4: 100 ) Let X denote the time to failure (in years) of a certain hydraulic component. Suppose the pdf of X is f ( x ) = 32 / ( x + 4) 3 for x > 0. (a) Verify that f ( x ) is a legitimate pdf. (b) Determine the cdf. (c) Use the result of part (b) to calculate the probability that time to failure is between 2 to 5 years. (d) What is the expected time to failure? (e) If the component has a salvage value equal to 100 / (4 + x ), when its time to failure is x , what is the expected salvage value? 2. ( Chapter 4: 106 ) The reaction time(in seconds) to a certain stimulus i a continuous random variable with pdf f ( x ) = 3 2 x 2 1 x 3 otherwise (a) Obtain the cdf. (b) What is the probability that reaction time is at most 2.5 sec? Between 1.5 and 2.5 sec? (c) Compute the expected reaction time. (d) Compute the standard deviation of reaction time....
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