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Let T be a continuous random variable denoting the time (in minutes) that a students waits...

Let T be a continuous random variable denoting the time (in minutes) that a students waits for the bus to get to school in the morning. Suppose T has the following probability density function:

f ( t ) = 1/10 ( 1 − t/30 ) 2 , 0 ≤ t ≤ 30.

(a) Let X = T/30 . What distribution does X follow? Specify the name of the distribution and its parameter values.

(b) What is the expected time a student has to wait for the bus in the morning? (Hint: use your findings in part (a).)

(c) Derive the cumulative distribution function of T .

(d) Suppose a student has already been waiting for the bus for 10 minutes. What is the probability that she will be waiting for at least 20 minutes?

Math   Statistics-And-Probability   
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