A Bayesian Solution to the Monty Hall Problem

The Monty Hall problem was created by Steve Selvin and is a classic puzzle whose correct answer is counter-intuitive almost to the point of disbelief. As this page explains, even some of the most competent mathematicians of the 20th century refused to accept the correct answer to the Monty Hall problem for a long time.

Here is the statement of the problem :

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the other two doors are goats. You pick a door, and the host, who knows what’s behind the doors, opens another door, revealing a goat. He then says to you, “Do you want to change your selection?” Is it to your advantage to switch your choice?

Monty Hall Problem. Image is from wikipedia

Monty Hall Problem. Image is from wikipedia

What does intuition tell us? After the host opens one door, revealing a goat, we are left with two closed doors, one hiding a car and the other a goat (50% chance of success either way), intuition would lead us to conclude that there is no difference in our chances of success if we switched doors or not.

If only life were that simple………….

Continue reading

Removing Noise : The Versatile Complementary Filter

After playing around with DC electronics for almost a year now, I thought it was finally time to start mucking about in the world of Alternating Current. To begin, I decided to experiment with the ACS712 Current Sensor.

ACS712 Hall Effect Current Sensor

ACS712 Hall Effect Current Sensor

Continue reading

Capturing the Elusive Analemma

This image, taken from Visakhapatnam (17 40 N 083 17 E), is possibly the first recording of the Analemma of the Sun ever captured in India. It combines a sequence of 26 individual photographs taken from 24 March 2013 to 13 March 2014. Superimposed over each other, they demonstrate the movements of the sun through the sky over a full calendar year. Click on the image for a larger view.

Analemma of the Sun

Analemma of the Sun

I photographed this sequence using a Nikon D40x camera and a variable ND filter, adjusting filter density, shutter speed and aperture settings at each instance to captureĀ  only the sun’s disc, leaving the rest of the frame completely black. The final image combines all 26 exposures with a background shot I took later.

Continue reading