Archive for Easter

pure birth process

Posted in Statistics with tags , , , , , , on April 18, 2020 by xi'an

The Riddler has a rather simplistic riddle this week since it essentially asked for the expectation of a pure birth process (also known as the Yule process) at time t. Since the population size at time t has a geometric distribution with expectation

eλt.

It however took me a while to recover this result on my own on Easter afternoon, as I went for the integrals rather than the distribution itself and the associated differential equations. Interestingly (in a local sense!), I first following the wrong path of looking at the average time to the first birth, 1/λ, then to the second, 2/λ, and so on. Wrong since of course expectations do not carry this way… For a unit rate,  λ=1, the average time to reach 10 births is about 3, while the average number of births over t=3 is essentially 20.

impressions, Barbizon [jatp]

Posted in pictures, Running, Travel with tags , , , , , , , on April 22, 2019 by xi'an

Somme graves

Posted in Kids, pictures, Travel with tags , , , , , , , on April 9, 2016 by xi'an

As mentioned in a previous post, we ended up spending Easter break in the Somme, close to the part of the Western Front that opposed German and Franco-British armies  between 1914 and 1918, with horrendous human losses: the first day alone of the Battle of the Somme in July 1916 saw around 60,000 British casualties! For a final gain of less than 10 kilometres… And a total number of dead close to a million. Unsurprisingly, the area is speckled with war cemeteries and memorials. Including an Australian National Memorial which commemorates the 16,000 Australian dead during World War I, including 11,000 with unmarked graves.  As for the cemeteries near the D-day beaches, I am always deeply moved when visiting war cemeteries, uncomprehending the waste of innumerable live of young men by military stratèges unable to adapt to new forms of warfare and throwing waves of foot soldiers against impregnable machine gun nests.

When running this weekend in the quiet and green Somme countryside, surprising a young deer which fled across the immense plain, with only a few bare thickets here and there, I was also wondering at how hellish was the place a hundred years ago, at how unworldly it should have looked to the entrenched soldiers, and whether or not any of this region had kept anything in common with the pre-war era, since entire villages were more than flattened, as shown by the picture of Guillemont below…

hot X buns

Posted in Kids, pictures with tags , , , , , on April 6, 2015 by xi'an

hotXbun1Since this is Easter weekend, and given my unreasonable fondness for hot-cross buns all year long, I tried to cook my own buns tonight, with a reasonable amount of success (!) given that it was my first attempt. I found an on-line recipe, mostly followed it, except that I added the yolk mixed with sugar to make the buns brown and shiny et voilà. If I ever try again to make those buns, I will look for an alternate way to make the [St. Andrew’s] crosses!

hotXbun2hotXbun3