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Formulas
Now there are a couple of nice formulas which we will get useful in a couple of sections. Consider that these formulas are only true if starting at i = 1. You can, obviously, derive other formulas from these for different starting points if you require to.
Here is a quick illustration on how to use such properties to quickly calculate a sum that would not be easy to do through hand.
#quesSuppose we have a stick of length L. We break it once at some point X ~ Unif(0;L). Then we break it again at some point Y ~ Unif(0;X). Use the law of iterated expectation to c
A function is an equation for which any x which can be plugged into the equation will yield accurately one y out of the equation. There it is. i.e. the definition of functions w
Subjective Probability Probability may be determined by a personal statement of how likely an outcome is in a single trial or repetition of the same experiment. Since sub
Example of division of fractions: Example: (4/5)/(2/9) = Solution: Step 1: Invert the divisor fraction (2/9) to (9/2). Step 2: Multip
Rates of Change and Tangent Lines : In this section we will study two fairly important problems in the study of calculus. There are two cause for looking at these problems now.
Find the derivatives of the following functions a) y = 5x 4 +3x -1-x 3 b) y = (x+1) -1/2 c) y= e x2+1 d) y= e 3x lnx e) y =ln(x+1/x)y
Determine or find out if the following series is convergent or divergent. Solution In this example the function we'll use is, f (x) = 1 / (x ln x) This function is
Consider the integral where the notation means a contour that is parallel to the real z axis, but moved down by a distance d . Use the method of steepest descents to deri
Fermat's Theorem If f(x) has a relative extrema at x = c and f′(c) exists then x = c is a critical point of f(x). Actually, this will be a critical point that f′(c) =0.
A company makes 2 products, Product A and Product B. The product characteristics are shown in the following table. Product A B
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