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Showing posts from September, 2013

### The Best Books for Linear Algebra

The following are some good books to own in the area of Linear Algebra. Linear Algebra (2nd Edition) This is the gold standard for linear algebra at an undergraduate level. This book has been around for quite sometime a great book to own. Linear Algebra: A Modern Introduction Good book if you want to learn more on the subject of linear algebra however typos in the text could be a problem. Linear Algebra (Dover Books on Mathematics) An excellent book to own if you are looking to get into, or want to understand linear algebra. Please keep in mind that you need to have some basic mathematical background before you can use this book. Linear Algebra Done Right (Undergraduate Texts in Mathematics) A great book that exposes the method of proof as it used in Linear Algebra. This book is not for the beginner though. You do need some prior knowledge of the basics at least. It would be a good add-on to an existing course you are doing in Linear Algebra. Linear Algebra, 4th Ed

### Estimating Unseen Bugs in Software

Follow @ProbabilityPuz Q: Two engineers independently do quality assurance testing a large swath of code and discover $$e_1$$ and $$e_2$$ number of bugs of which $$e_c$$ are common to both. The probability that each of them would find a bug given a large swath of code is $$p_1$$ and $$p_2$$ respectively. What is your best estimate of the number of unseen bugs in the code? Toshiba Satellite C55D-A5240NR 15.6-Inch Laptop (Satin Black in Trax Horizon) A: This puzzle is inspired from W Feller's book on introduction to probability. The total number of unique bugs identified are $$e_1 + e_2 - e_c$$. Let $$B_0$$ represent the total number of bugs in the software application. We could make the following statements $$e_1 = p_1 \times B_0 \\ e_2 = p_2 \times B_0 \\ e_c = p_1 p_2 \times B_0 = \frac{e_1 e_2}{B_0}$$ The unseen bugs are simply $$\text{Unseen Bugs} = B_0 - (e_1 + e_2 - e_c)$$ Combining the above two equations yields  \text{Unseen Bugs} = \frac

### Blending Expert Estimates

Follow @ProbabilityPuz Q: You have a diamond but are not sure whether its a real or a fake one. You show the diamond to two experts who independently estimate the probability that it is real at $$p_1$$ and $$p_2$$. What is your estimate of what the true probability is? Canon EOS Rebel T3 12.2 MP CMOS Digital SLR Camera with EF-S 18-55mm f/3.5-5.6 IS II Zoom Lens & EF 75-300mm f/4-5.6 III Telephoto Zoom Lens + 10pc Bundle 16GB Deluxe Accessory Kit A: Surprisingly, there is no clear answer or strategy on how to approach and blend such subjective estimates together. Most people run into similar situations all the time wherein they get estimates from different sources on a fixed decision they need to make. A naive way to approach this would be to average the two estimates. This would yield $$\frac{p_1 + p_2}{2}$$ in the present case. But this doesn't address all the cases. For example if $$p_1 = p_2 = 0.6$$, i.e. the experts agree independently the overall estim