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Conditional probability mass function of the sum of independent geometric random variables.

$X, Y \sim Geom\left(p\right)$, and $X, Y$ are independent. Find $p_{X | X+Y}\left(i | n\right)$. My approach: pmf of geometric distribution: $p_X(i) = {p(1-p)^{i-1}}$ Then, by the law of total probability: $p_{X | X+Y}\left(i | n\right) = \frac{p_{X, X+Y}\left(i,n\right)}{p_{X+Y}\left(n\right)} $ [Is using the law of total probability here correct as opposed to using Bayes theorem?] […]

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Law of Cosines and Heron’s Formula in inequalities

I had the following question: Suppose $a$, $b$, and $c$ are non-zero real numbers, and $x$, $y$, and $z$ satisfy the equations $$ bx + ay = c, cx + az = b, cy + bz = a. $$ Prove that $-1 < x, y, z < 1$ if and only if $a^4 + b^4 […]

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Different shape arrays operations

A bit of background: I want to calculate the array factor of a MxN antenna array, which is given by the following equation: Where w_i are the complex weight of the i-th element, (x_i,y_i,z_i) is the position of the i-th element, k is the wave number, theta and phi are the elevation and azimuth respectively, […]

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Calculate the Taylor Polynomial

Question Question I need help with the cosh(x) def taylorCosh(x, n): y = 0 for k in range(n): y += (x ** (2 * k)) / (math.factorial(2 * k)) return y nVariables = [1, 2, 3, 4, 8, 16, 32, 64, 128, 256] xVariables = [(1/32), (1/16), (1/8), (1/4), (1/2), 1, 2, 4] x_pos=0 for […]