From b1f4f78a573a1f8a909560486a5da20c975a7d18 Mon Sep 17 00:00:00 2001 From: Claire Wang <41759033+ClaireBookworm@users.noreply.github.com> Date: Sat, 19 Oct 2019 13:47:24 -0700 Subject: [PATCH] Update README.md --- README.md | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/README.md b/README.md index fda46c1..d728595 100644 --- a/README.md +++ b/README.md @@ -4,3 +4,10 @@ Here is the frog problem code I wrote in an Edinburgh pub. Feel free to make better version. This one has not changed since I wrote it. V1 was the same code but saved before I changed it to work for different distances so I have not bothered upload it as well (it was still very unifinished). Video is here: https://youtu.be/ZLTyX4zL2Fc + +## The problem + +A frog is on one side of the pond and wants to get on the other side. There are 𝑛 lily leaves ahead in a line, the 𝑛-th leave laying on the other end of the pond and being the destination. Whatever the position the frog is at any time, it will only go ahead and the probability to land on one of the leaves left in front of it (including the destination) is uniform. For example, if we have 10 leaves ahead, there is a probability of 110 that it will land on any of them. + +a) What is the expected value for the number of jumps it will take the frog to arrive to the destination leaf? +b) Can you come up with a formula for that? (It can't be a recursive expression...)