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The most common and basic mistake which I saw people with poor knowledge of statistics make is to apply different ML tools on data without understanding the importance of dimensionality constant and data’s probability distribution.1. Dimensionality constant and the Curse of Dimensionality: Dimensionality constant gives a metric to understand if enough data is available to apply a certain statistical algorithm. It is basically related to the size of the data matrix. If there are 100 features (say 100 stocks from S &P) and 500 samples (500 daily return values of each stock), then the size of the data matrix will be 100 x 500 and dimensionality constant will be 100/500 = 1/5. This also means that in given 100-dimensional feature space, each basis feature has 500 samples located in that 100-dimensional space. The value of dimensionality constant can greatly affect the performance of any statistical tool. Most of the derived multivariate asymptotic results in statistics assume that dimensionality constant is close to zero (i.e. both number of features and number of samples are asymptotically large but the number of samples is much larger than the number of features). The most widely used methods like multivariate regression also perform well only under this condition. This simply means that it is important to have enough samples for each feature to accurately understand the role of that feature in regression or any other statistical setup.If the dimensionality constant is too large, it means that there are more features but samples per features are very less. In this case, commonly applied methods like covariance analysis, PCA, linear regression, etc. can give highly inaccurate results. There is a whole field dedicated to deriving results when enough samples per feature are not available. In fact, as the number of features (or dimensions) increases, the total number of samples required increases exponentially. This is also studied under the topic called the Curse of Dimensionality! This can be easily seen from the above image[1][1][1][1]which shows that as the dimension increasesl from 1D to 3D, more samples are required to explain the basic useful geometrical information.The best theoretical case will be that dimensionality constant is close to zero but this is not always good for real-world applications. For example, in case of financial data, if we will take many years of daily return (i.e. a large number of samples for each stock) then it can give misleading correlations and information. Many financial applications require to only consider recent data to avoid including bias from history. In such a case, dimensionality constant approaching to one can be better than zero. So, it is crucial to decide what is the desired number of samples per feature for the given application. So, sometimes right number (range) of samples are required to correctly model correlations among multivariate data (not too many and not too less).2. Normality of data: Most of the widely used ML algorithms including most famous ones like linear regression requires error (or noise) distribution to be Gaussian distributed. Have a look at following three histograms which represent the same data. The data[2][2][2][2] is the noise samples from underwater measurement in an urban water supply system pipeline (it was collected by me).The first image shows the histogram of noise samples with both x and y-axis in linear scale. At first glance, the data looks nearly gaussian. In the second image, I overlapped a Gaussian density curve (dotted red line) with the same mean and variance as the noise data. Now, it can be seen that data histogram is not perfectly Gaussian and there is a little deviation from gaussianity (blue curve different from the red curve). In the third image, I changed y-axis from linear to log scale. Now, it can be seen that there is a huge difference in the shape of the noise data histogram and gaussian distribution. The tails of the data are significantly diverging from the gaussian nature. It turns out that a much complex class of distributions known as alpha-stable distribution perfectly fits this noise histogram[3][3][3][3]. This is the case of heavy-tailed data distribution which is looking almost gaussian in linear scale but after superimposing gaussian curve and changing from linear to log scale, it turns out to be much different from a gaussian distribution. In fact, the heaviness of tails in the above case is quite huge and collecting more samples shows that the tails of the data distribution decay much slower than the Gaussian distribution even for very large values of noise amplitudes. This means that the probability of seeing outliers (outside gaussian curve) is significant even at very large noise amplitudes.Applying standard signal processing or ML algorithms which are optimally derived for gaussian nature of data can be suboptimal in this case. In fact, for heavy-tailed distributions, the most commonly used tools like covariance analysis, PCA, etc are ineffective because the data with heavy-tailed distribution (like Cauchy, alpha-stable, etc) have extremely high variance (theoretically infinite variance) which leads to undefined or highly unstable covariance.So, the common mistake here is to interpret any bell-like curve as gaussian which might be far from reality. The first step should be to use standard tests like Kolmogorov–Smirnov test to check the nature of the distribution. If the sample size is too small then even these tests are not reliable and if the sample size is too big (like in the above image, there are around 10 million samples) then these tests might take hours to give results. In such scenarios, small tricks like overlapping standard density curves on the empirical distribution or changing scales of the y-axis might give a better and quick approximation.3. Histogram, normalized histogram and probability density function (pdf): In any programming language, there are multiple options to select the “type” in the argument of histogram function. This is important. In the default setting, the y-axis of histogram simply represents “relative frequency” or “normalized count”, i.e. y-axis value for each bin represents “discrete probability mass” (occurrence of certain event in that bin width/total occurrences). This means that the y-axis values of all bins should give one on summation. This is also called relative frequency histogram. Another type of histogram is called probability density histogram in which the y-axis value of each bin gives “density” value rather than probability mass. This means y-axis value of each bin is equal to (discrete probability mass or normalized count)/bin width. For this type of histogram, the total area of all the histogram bars should sum to one. Finally, the last type is called probability density function (pdf) which is a continuous function and provide density at each value of a random variable (RV). The pdf usually have an analytical expression with few parameters to control its shape and properties. The total area under this function curve should integrate to be one.To sum up, the first type of histogram simply tells us how many incidences of event occurred inside a bin and this count is divided by total incidences to get normalized count. The second type goes one step further and divide the normalized count by bin width to get the probability density instead of probability mass. The last one is a theoretical continuous function and completely describes a RV (few exceptions).The biggest mistake made by the beginners is to overlap theoretical pdf over relative frequency histogram. An empirical histogram can be compared to the theoretical pdf only if the histogram is of “density” type rather than the normalized count type.Some other common mistakes are:4. Ignoring sampling error[4][4][4][4]5. Choosing the wrong Loss function[5][5][5][5]6. Correlation vs Causation[6][6][6][6]Footnotes[1] Escaping the Curse of Dimensionality[1] Escaping the Curse of Dimensionality[1] Escaping the Curse of Dimensionality[1] Escaping the Curse of Dimensionality[2] Measurement and Characterization of Acoustic Noise in Water Pipeline Channels[2] Measurement and Characterization of Acoustic Noise in Water Pipeline Channels[2] Measurement and Characterization of Acoustic Noise in Water Pipeline Channels[2] Measurement and Characterization of Acoustic Noise in Water Pipeline Channels[3] Measurement and Characterization of Acoustic Noise in Water Pipeline Channels[3] Measurement and Characterization of Acoustic Noise in Water Pipeline Channels[3] Measurement and Characterization of Acoustic Noise in Water Pipeline Channels[3] Measurement and Characterization of Acoustic Noise in Water Pipeline Channels[4] http://www.cs.cmu.edu/~tom/10601_sp08/slides/evaluation-2-13.pdf[4] http://www.cs.cmu.edu/~tom/10601_sp08/slides/evaluation-2-13.pdf[4] http://www.cs.cmu.edu/~tom/10601_sp08/slides/evaluation-2-13.pdf[4] http://www.cs.cmu.edu/~tom/10601_sp08/slides/evaluation-2-13.pdf[5] 5 Regression Loss Functions All Machine Learners Should Know[5] 5 Regression Loss Functions All Machine Learners Should Know[5] 5 Regression Loss Functions All Machine Learners Should Know[5] 5 Regression Loss Functions All Machine Learners Should Know[6] Correlation is not causation[6] Correlation is not causation[6] Correlation is not causation[6] Correlation is not causation

The success of the PDF file format is a great example of how a product becomes a global technical standard. For anyone looking to build or invest in a new technology that hopes to become a standard, I can't think of a better lesson from history. In the early 90s, the PDF was competing against several other file formats including DjVu, Envoy, Common Ground Digital Paper and Adobe's own PostScript format (referencing the question).In its earliest days, the PDF solved a simple but important problem: a PDF looked exactly the same everywhere, regardless of which device opened the file. This is why PDF stands for Portable Document Format. As Abhishesh has written, this was a big deal in a world where font recognition was an issue. The PDF was the first file format that enabled a document to be shared electronically while retaining all elements of its original formatting. If the sender sends a PDF, he or she has full confidence that the recipient will be able to read the file. Today, this seems relatively trivial as cross-device readability for many different file formats is not a big deal.But the PDF file didn't succeed because of its technical prowess, it succeeded because of Adobe's strategic foresight. In fact, there are good arguments for why other competing file formats were technically superior to the PDF. While Adobe initially charged $50 for Adobe Reader in 1993, it quickly realized this was a mistake and made the product free in the same year. By distributing Adobe Reader free of charge (unlike any of its competitors), the PDF quickly gained adoption. By 1999, more than 100 million copies of Adobe Reader had been downloaded from the web, and the PDF became a global standard.

Before appearing for any exam, we must first understand what it demands. Each exam is unique and hence asks for a specialized approach. Same goes for RBI Grade B exam. The exam is quite straightforward but seats being so less ( Seats in Generalist UR category were a mere 64 in 2018) makes the exam one of the toughest in India. Also by cracking it you get a opportunity of working in the Central Bank of the nation. That itself is a strong motivating factor.Coming to the preparation front now,Phase -1/Prelims: It has 4 sections. Reasoning (60) + Quants (30) + English (30) + General Awareness (80)For the first 3 sections the preparation is ditto as applicable for a Bank PO, Insurance AO exam. As I was short on time, I just prepared for these sections through mock tests only (From Oliveboard, Practicemock). For GA refer toBankersAdda Hindu Review (last 6 months)GKtoday 250 Questions monthly pdf (last 6 months)Affairscloud 100 Questions monthly Pocket Booklet (last 6 months)Any standard static GA booklet. (I referred to Bankers Adda’s).In prelims, GA is the deal-maker or deal-breaker. I knew that GA held the key. So I put in that extra effort to strengthen my GA. Seems my choice paid off as I got 55.75/80 in GA and 132/200 overall in Prelims.Now coming to Phase -2/MainsFor ESI, I referred to the following sources:1. Edutap ESI static module2. Gktoday monthly pdf (detailed one) (last 8 months)3. Vision IAS monthly GA pdf ( Only Economics and Social part) (last 8 months)4. Union Budget (from original document)5. Economic Survey Vol.I (from MoFinance website)6. Govt Schemes pdf from Vision IAS.In ESI, a lot of questions are coming from Govt. Schemes. Questions are being asked even from 1999, 2005 schemes. So mark this as an important area. Marks secured (78.25/100)For FM , I referred only to Edutap’s FM static module. Especially the Numericals part wherein I got a really good hang of things as everything was explained so lucidly. I also went through the RBI notifications that came out on the official website and felt had a relevance to the exam. Investopedia also proved to be a handy tool for reference. Marks secured (79/100)For English Descriptive paper in Mains, there is no need to explicitly prepare for it. Fodder material for Essay will already be prepared through your ESI+FM prep. Just practise 2 Essay, 2 Preci and 1 Comprehension before exam day. That would be sufficient. Marks secured (65/100)For interview, I just went through a financial newspaper on a daily basis and brushed up on my profile and banking basics. Marks secured (31/50)Total Marks: (253.25/350) which gave me an AIR of 37.That’s how I prepared for RBI Grade B folks. Best of luck to you all!