Pickwick’s Umbrella
In London, half of the days have some rain. The weather forecaster is correct 2/3 of the
time, i.e., the probability that it rains, given
that she has predicted rain, and the
probability that it does not rain, given that she has predicted that it won’t rain, are both
equal to 2/3. When rain is forecast, Mr.
Pickwick takes his umbrella. When rain is not forecast, he takes it with probability 1/3.
Can you find
(a) the probability that Pickwick has no umbrella, given that it rains.
(b) the probability it doesn’t rain, given that he brings his umbrella.
This problem apears in
K. L. Chung, Elementary Probability Theory With Stochastic Processes, 3rd ed. (New York:
Springer-Verlag, 1979), p. 152
NOTE: You may not assume that the probability that she predicts rain is 1/2
or that the probability that she predicted rain given that it rains is 2/3; however, you need that, so prove it first.
HINT: Show that for any two events R & F such that a = P(R|F) = P(~R|~F)
P(F) = 1 - (a +P(R)) ,
1 - 2a
a ≠ ½ and under the further constraints that place the RHS between
0 and 1 inclusive.
When P(R) = ½ a drops out of the RHS and P(F) = ½ .
That day I was walking along
the beach at Zandvoort; the sky was filled solid with white clouds and several seagulls were gliding in the gentle wind.
As I walked I thought about
myself and asked a funny question of God. I asked,
“Well, just where do I stand in the great scheme of things, how do I rate?”
Just then the sky opened up
and a strong beam of sun shone squarely on a seagull above me
and towards the sea, about
120 feet away.
The gull was white but
now all that I could see was a massive, golden array of rippled muscles forming his chest, back, and left wing.
As his wings gracefully moved,the muscles continued to shine brightly in the newly forming blue sky;
and with great freedom and command of his world,
he flew off.
And I thought to myself,
so that’s it, I’m no better than a lowly gull.
http://www.youtube.com/watch?v=bcPh9z7gm6s&feature=g-tvshow&list=SL
HAPPY NEW YEAR 2012
A point in time when we decide on doing new and better things to improve and cast away thoughts of the older ones; especially those that didn't work well. And to those that drew blanks, maybe reconsideration, maybe now it’s their time. One thing is certain, though, it’s your time.
Or is it?
I had a thought late last night that about the only fate for the Euro is to split into 3; one NE Northern Euro for mainly France and Germany,
one SE Southern Euro for mainly Spain, Italy, and Greece; and one EE, Eastern Euro, for the the others not covered.
The problem with the Euro today is the differences in cultures and languages of the EU prevents a united monetary policy. Dividing the currency, and policy, into pieces that belong to like cultures and languages will work splendidly. However, that's not what Europe wants! It foolishly is trying to mimic the US. It can't - because the US has only one culture, one language.
If the triad is done, the NE will be strongest, say at 1.1 / $; then the SE at 1.0; and then the EE at .9. That gives the underdeveloped, weaker regions an advantage on exports and tourism - which account for most of their GDP.
I think the reversion to individual currencies for each country will never happen.
In the meantime, look for the Euro to approach the 1.1 / $ by summer. That's a decrease of around 15% from today's rate. EUO will increase by 30%.
Happy New Year
Dan
Contact Dan DuPort at
