alice and bob each choose a random number between 0 and 2. We assume uniform probability law under which the probability is proportional to its area. What is the magnitude of difference of the two numbers is greater than 1/3
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Alice and Bob each choose a number uniformly at random from the interval \([0, 2]\). The sample space is the square \([0, 2] \times [0, 2]\) with area \(2 \times 2 = 4\). Show more…
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Alice and Bob are trying to meet for lunch and both will arrive, independently of each other, uniformly and at random between noon and 1pm. Let A and B be the number of minutes after noon at which Alice and Bob arrive, respectively. Then A and B are independent uniformly distributed random variables on [0, 60]. [Hint] Find the fraction of the square [0, 60] x [0, 60] filled by the event. 1) Find the joint pdf f(a, b) and joint cdf F(a, b). 2) Find the probability that Alice arrives before 12:30. 3) Find the probability that Alice arrives before 12:15 and Bob arrives between 12:30 and 12:45 in two ways: i) By using the fact that A and B are independent. ii) By shading the corresponding area of the square [0, 60] x [0, 60] and showing that the proportion of shaded area equals the probability. 4) Find the probability that Alice arrives less than five minutes after Bob. 5) Now suppose that Alice and Bob are both rather impatient and will leave if they have to wait more than 15 minutes for the other to arrive. What is the probability that Alice and Bob will have lunch together?
Sri K.
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Ivan K.
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