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Q. A jar has a single cell of a bacteria. After every fixed interval of time the bacteria either splits into two with probability 2/5, does nothing with probability 2/5 or dies out with probability 1/5. What is the probability that the bacteria would continue to make a large family tree over an extended period of time? A. The situation can be described by the following visual. Assume that the required probability is 'p'. The term 1 - p would represent the probability that the ecosystem eventually dies out. Each of the above scenarios contributes a quantum of probability towards the ecosystem eventually dying out. Lets start off by represent 1 - p as 'x'. The probability that the bacteria die out is The total of each of the above must add up to the probability that the bacteria eventually die out, which is 'x'. So you can phrase the problem recursively as This simplifies to which is a quadratic equation, yielding a solution as This

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Often times a lot of people working with data are trying to create an index of some sort. Something that captures a set of key business metrics. If you are a site (or an app) you want to create some sort of an engagement index, which if trending up implies good things are happening, bad if it is trending down. The creators of such metrics (think analysts) tend to prefer a weighted arithmetic mean of the influencing factors. If the influencing factors are f1,f2, f3 (say) with weights w1, w2, w3 then the index would be computed as However, what does not get factored in are the final consumers of the index (think product managers) and there could be many. They will invariably try to check it with something else they have handy. For example, if clicks on a site went up 20% the index may be up by just 5% (say) or vice-versa. If resources are being allocated based on the movement of such an index, it will invariably lead to contention on what is the right weighting to be given to each f

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Q: You have a set of thirty six cards. The cards are six in color ( six each) and each color is numbered from 1 to 6. You draw two cards at random. What is probability that they are of a different color and have a different number? A: The first card can be drawn at random. It does not matter what its color or number is. To compute the probability that the second card is different in color and number from the first, it helps to visualize the situation in a simple way as shown below. In the figure above, assume the green dot represents the card that was picked. The marked out cards represent the cards that should not be picked to get a different color and number. Also, the act of picking a card bought down the pool of cards from 36 to 35. The remaining unmarked space represents the available set of cards to pick from. This can be computed easily as This yields an overall probability of If you are interested in learning the art of probability, some of the best book

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Python is a great programming language. It's primary merits are readability and the numerous packages that are available online. However, being an interpreted language the speed of execution is always an issue. Here is a simple example of a piece of code written in Python that tries to add two numbers from a grid. #!/usr/bin/python def overlap_pp(x,y): count = 0 for i in range(x): for j in range(y): count += i + j return count for _ in range(1000): q = overlap_pp(500,500) If you run the above script (saved as n.py) on the command line terminal with the time command you should see some numbers like the below time ./n.py real 0m22.379s user 0m22.363s sys 0m0.407s The process running on one processor took about 22 seconds to complete the run. Now lets do something seemingly magical. Lets add a decorator. Decorators are python speak for a mechanism to do wrapper functions. The decorator we are going to add is '@jit'. The code looks l

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