The Monty Hall problem is an interesting puzzle loosely based on an American TV game show Let’s Make a Deal hosted by Monty Hall. While the puzzle looked simple, it perplexed some of the brightest mathematical minds in the United States, including the great Paul Erdös who was one of the most prolific mathematicians of the 20th century. This continues to be the case today. I looked upon a number of references to find the source of confusion in the Monty Hall problem but failed. All I found was different solutions. Therefore, I built one myself with the usual from
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Cascaded Integrator Comb (CIC) Filters – A Staircase of DSP
In olden days, people used to have lots of kids. A famous Urdu satirist once wrote: "It has been observed that the last kid is usually the most mischievous of them all. Therefore, there should be no last kid in a family!" I remembered this line today because I have observed that starting a write-up is the most difficult task of them all. Therefore, there is no introductory paragraph in this article. Suffice it to say that this is the only topic I have found that takes you from a very small first step (just two additions) to really advanced
Continue readingAn Intuitive Guide to Linear Regression
We have described before how supervised learning can help us predict a continuous-valued output or organize the input into discrete categories, commonly known as regression and classification problems, respectively. In this article, we describe linear regression and leave the classification algorithms for a future post. What is Linear Regression? Suppose that you are a young investor living in a region with cold climate. One day an idea flashes in your mind that perhaps the shares in the regional stock market climb linearly with the temperature: the better the weather, the higher the prices. You already know what the temperature is
Continue readingThe Coin Toss Puzzle and the Simplest Possible Solution
Recently, I wrote an article on why the Monty Hall problem has perplexed so many brilliant minds where I showed that it was a corner case between 1 open and 1 closed door, while the intuitive but wrong answer is close to the probability curve of 1 open door. Now a coin toss puzzle has appeared on Twitter that has gone viral as it goes against our common intuition of probability and random sequences (such as a series of coin tosses). The puzzle goes as follows. The Problem Flip a fair coin 100 times—it gives a sequence of heads (H)
Continue readingCoordinate Rotation Digital Computer (CoRDiC)
Digitial Signal Processing (DSP) plays a crucial role in algorithm implmentation for building digital and wireless communication systems. A common theme in all those algorithms is that they can be implemented with the following simple operations: addition multiplication shift In fact, these are the basic principles on which a digital signal processor is constructed. However, when it comes to implementation of real-time systems in hardware such as FPGAs, we find ways to reduce the complexity even further. Which operation (out of the above three) do you think is the most demanding in computations? It is the multiplications. Therefore, it is
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