Continuous Computations
Let X be a continuous random variable whose pdf is cx3 (for some constant c) in the range 0 ≤ x ≤ 1, and is 0 outside this range.
(a) Find c.
(b) Find P[1/3 ≤ X ≤ 2/3 | X ≤ 1/2].
(c) Find E(X).
(d) Find var(X).
CS 70, Fall 2018, DIS 12A 1
2 Lunch Meeting
Alice and Bob agree to try to meet for lunch between 12 PM and 1 PM at their favorite sushi restaurant. Being extremely busy, they are unable to specify their arrival times exactly, and can say only that each of them will arrive (independently) at a time that is uniformly distributed within the hour. In order to avoid wasting precious time, if the other person is not there when they arrive they agree to wait exactly fifteen minutes before leaving. What is the probability that they will actually meet for lunch?
3 First Exponential to Die
Let X and Y be Exponential(λ1) and Exponential(λ2) respectively, independent. What is
,
the probability that the first of the two to die is X?
