87 more posts in this thread. [Missing image file: 1350239830138.jpg]
Well hello there /sci/...
It's been awhile since I've posted, and I finally have some down time, allowing me to post again.
Would any of you fine, aspiring scientists need any textbooks for your upcoming semester? If any of you remember my thread earlier this year, you know I'll do my best to deliver your request.
11 more posts in this thread. [Missing image file: Jim.jpg]
Hi /sci/, I have a math puzzle for you.
Jim lost his glasses.
He can't see well without his glasses so he can only tell if they're directly under him.
His glasses are somewhere along an infinitely long line.
The probability distribution of his glasses is the standard normal distribution,
P(x) = 1/sqrt(2*pi) e^(-1/2 x^2)
Starting at the position x=0, Jim wants to minimize the average distance he must walk to find his glasses.
So What is the sequence of positions for Jim to walk to which minimizes this?
For example, if Jim walks to the positions
0.01, -0.02, 0.03, -0.04, 0.05, ...
he's walking a lot to cover a small space cause he keeps walking over what he already covered.
However, if he walks to the positions
1000, -2000, 3000, -4000, 5000, ...
there's a good chance his glasses are close to 0 but negative, and he'll be walking way more than he needs to.