Class Notes (835,638)
United States (324,200)
AMS 5 (51)
Lecture 16

# AMS 5 Lecture 16: Class 16 - The Central Limit Theorem Premium

2 Pages
100 Views

Department
Applied Math and Statistics
Course
AMS 5
Professor
Yonatan Katznelson
Semester
Spring

Description
AMS 5 Lecture 16 5122017 (8:009:05) The Central Limit Theorem (CLT) n tickets are drawn at random with replacement from a box of tickets with avg = A and SD = s o Expected value of the sum EV(Sum) = n*A o Standard Error of the sum of the draws: SE(Sum) = n 12* s o Box of sums: tickets labeled with sums of all possible draws of n tickets from the average box. o Avg(Box of sums) = n * A = E U (Sum) o SD(Box of sums) = n 12* s = SE(Sum) CLT If n is large enough, then the box of sums has an approximately normal distribution Browninan Motion Botanist in 1950s who was studying jar of pollen, and in jar he saw the pollen was moving, and the movement looked random, however it didnt stray too far from the original observed area. Its moving because the water molecules are moving and striking the pollen in all directions, trying to force it to equilibrium. Example: Box has an average of 10 and a SD of 2. n = 10000 tickets are drawn at random with replacement from this box. o EV(Sum) = 10*10000 = 100,000 o SE(Sum) = (10000) *2 = 200 o Expect sum to be about 100000 + 200 (law of averages) o P(99600 <= obs sum <= 100400) = ? P( obs sum EV < 400) = P( obs Avg < 230) ~ 95 o More generally: P(A < obs sum < B) = Convert to standard units
More Less

Related notes for AMS 5
Me

OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Join to view

OR

By registering, I agree to the Terms and Privacy Policies
Just a few more details

So we can recommend you notes for your school.