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What probability distribution best describes the place of a dart?

It depends on factors such as precision and accuracy. If the dart is precise but not accurate, you’ll get a bivariate normal but not at the center. If it is precise and accurate, you’ll get a ...
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1 vote
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Compute expected value from two dimensional normal distribution

The term in the exponent of $f(x,y)$ can be written as $$\begin{split}-\frac 18\left[4x^2+8x(y+3)+6(y+3)^2\right] &= -\frac 12 \left[x^2+2x(y+3)+\frac 32(y+3)^2\right]\\ &=-\frac 12\begin{...
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1 vote
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Mean value of the derivation ReLU function with Normal Distribution

Because we have $$\int_{-\infty}^\infty relu’(x)f(x)dx=\int_{-\infty}^\infty I(x>0)N(0,\sigma^2)dx=\int_0^\infty N(0,\sigma^2)dx=\frac12$$ the answer is $\frac12$.
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