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Gloria and Steven are supposed to meet at 2 pm. The number of hours Gloria is...

Gloria and Steven are supposed to meet at 2 pm. The number of hours Gloria is late is distributed uniformly over (0,1). The number of hours Steven is late is distributed according to an exponential random variable with parameter 2. Their respective delays are supposed to be independent. Let X be the time at which Gloria and Steven actually meet (in number of hours after 2 pm).

A) Find the cumulative distribution function of X.

B) Use it to calculate the probability density function of X.

Math   Statistics-And-Probability   
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