Probability - Frequently asked questions

Assignment 1:

• Q: In question 48a, is the intention to calculate the probability that for *all* 1≤i<j≤k we require that |X(i)-X(j)| is not equal to n?

  A: The event we consider consists of those sequences in which no two entries differ by exactly n. For example, if n=4 and k=3, then the sequence 3, 5, 2 satisfies the required condition, while the sequence 2, 1, 6 does not (since 2 and 6 are at a distance of 4).

• Q: In assignment 2 in probability I couldn't quite understand what I need to do in question 101. Can you please elaborate?

  A: Consider the lazy secretary problem. Let k be an arbitrary fixed integer. We are interested in the probability that exactly k out of the n letters will be sent to the right destination. Now this probability depends also on n. The question is what happens to this probability as n grows to infinity.

• Q: In question 130 can we assume that U1 and U2 are chosen independetly?

  A:I don't think you need it, but in any case it follows from the fact that (U_1,U_2) is distributed uniformly in the square.