A college professor never finishes his lecture before the bell rings to end the period and always finishes his lecture with one minute after the bell rings. Let X the time that elapses between the bell and the end of the lecture and suppose that the p.d.f of X is: S(x) = kx(1–Jx). 0sxs1] f (x)=0, otherwise i. Find the value k. ii. What is the probability that the lecture ends with ½ minute of the bell ringing? iii. What is the probability that the lecture continues for at least 40 seconds beyond the bell ?
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A college professor never finishes his lecture before the bell rings to end the period and always finishes his
lecture with one minute after the bell rings. Let X the time that elapses between the bell and the end of the
lecture and suppose that the p.d.f of X is:
f (x) = kx(1–Jx). 0sxs1]
f (x)=0, otherwise
i.
Find the value k.
ii.
What is the probability that the lecture ends with ½ minute of the bell ringing?
iii.
What is the probability that the lecture continues for at least 40 seconds beyond the bell ?
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