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 |
Handnotes:
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
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