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Your driving time to work (continuous random variable) is between 29 and 65 minutes if the day is sunny, and between 44 and 81 minutes if the day is rainy, with a uniform probability density function in the given range in each case.
Assume that a day is sunny with probability = 0.13 and rainy with probability .
Your distance to work is = 50 kilometers. Let be your average speed for the drive to work, measured in kilometers per minute:
Compute the value of the probability density function (PDF) of the average speed at = 0.68
Round your answer to five decimal digits after the decimal point.
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