Mathematical Statistics

 

Lecturer Theory:

Lecturer Problems:

Timetable:

Classroom:

Tutorials:

Isabel Molina Peralta (10.1.18)

Leo Berbotto (10.1.20)

Monday 12-14h, Thursday 9:30-11:30h

Monday 11.1.30, Thursday 11.2.08

Monday and Tuesday, 11:00-12:00h

 

Course Guide

 

Handnotes:

 

Full material

 

Slides Chapter 1. Measure Theory and Probability

Slides Chapter 2. Convergence concepts

Slides Chapter 3. Laws of large numbers

Slides Chapter 4. Central limit and Slutsky’s theorems

 

Exercises to hand in:

 

Section

Problems

Deadline

1.1

5, 7

Thu, Sept. 30

1.2

4

Thu, Oct. 14

1.3

4

Thu, Oct. 14

1.4

1 (vii)

Thu, Oct. 21

1.6

2,5

Thu, Oct. 21

 

 

 

 

The Penrose stairs

image001.jpg

The Penrose stairs is an impossible object devised by Lionel Penrose and his son Roger Penrose and can be seen as a variation on his Penrose triangle. It is a two-dimensional depiction of a staircase in which the stairs make four 90-degree turns as they ascend or descend yet form a continuous loop, so that a person could climb them forever and never get any higher. This is clearly impossible in three dimensions; the two-dimensional figure achieves this paradox by distorting perspective.

The best known example of Penrose stairs appears in the lithograph Ascending and Descending by M. C. Escher, where it is incorporated into a monastery where several monks ascend and descend the endless staircase.

The staircase had also been discovered previously by the Swedish artist Oscar Reutersvärd, but neither Penrose nor Escher were aware of his designs.

Source: wikipedia