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Difference between at least and less than binomial probability
Got a two part question given to me (I used binomial Distribution to solve) If the probability that an individual moves outside of his or her country of r...
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Interpreting Game Theory Questions
I have come across two game theory questions, and got stuck in a similar stage in both. Problem 1: There are two boxes, correctly labeled as 4 candies and...
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Distance Between A Point And A Line
Any Hint on proving that the distance between the point $(x_{1},y_{1})$ and the line $Ax + By + C = 0$ is, $$\text{Distance} = \frac{\left | Ax_{1} + By_{...
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How do I solve $x^4 -2x^3-6x^2-2x+1=0$? [closed]
$$x^4 -2x^3-6x^2-2x+1=0$$ $\left[\text{Hint let } v = x + \frac{1}{x}\right]$ I am stumped, and have no idea how to proceed. I have tried solving it, but ...
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98% confidence interval
For this question from a large amount of data I have calculated that the mean is 44.22, the sample size is 100 and the standard deviation is 22.0773. From...
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Understanding the dihedral group
I know that the dihedral group is $$D_{2n} = \{1, r, r^2, \dotsc, r^{n-1}, s, sr, \dotsc, sr^n-1\}$$ where the $r^i$ are rotations and $s$ is a symmetry. ...
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Given preimage area of a triangle, find image triangle area after a transformation
Given transformation S: $$\begin{pmatrix} 3 & 2 \\ 4 & 2 \\ \end{pmatrix}$$ If a preimage triangle has an area of 10, what is the area of the imag...
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How to find the volume of a irregular tetrahedron, when I know the length of all sides?
What I have been told: There's a irregular tetrahedron(pyramid with a base of a triangle), I know that three edges that form the tip are of length 2(...
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Finding Bessel function $J_{1/2}$ using power series method.
The Bessel function $J_{1/2}$ is a solution of the differential equation: $$x^2 y '' + xy' +(x^2 - (1/2)^2)y = 0 $$ I am looking to find $J...
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Why does Benford's Law (or Zipf's Law) hold?
Both Benford's Law (if you take a list of values, the distribution of the most significant digit is rougly proportional to the logarithm of the digit...
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