# Questions tagged [calculus]

For statistical questions involving calculus. Please use also a more statistical tag. For purely mathemathical questions about the calculus, it is better to ask at math SE https://math.stackexchange.com/

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### Correlation between normal and log-normal variables

(This is not a homework question.) Let $(X_1 \sim N(\mu_1,\sigma_1), X_2 \sim N(\mu_2, \sigma_2))$ be a bivariate normal random variable with the correlation between $X_1$ and $X_2$ given by $\rho$. ...
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### Maths for deeply understanding backpropgation

I have been trying to develop a deeper understanding of Neural Networks so I can understand the libraries such as tensorflow and others. I have had good success with pereceptron models, and have a ...
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### How does one compute a variational derivative?

The expected regression loss is given as:$$E[L]=\int\int \{y(\mathbf x)-t\}^2 p(\mathbf x,t)d\mathbf xdt$$ To minimise the expected loss,Euler Lagrange equation is used which goes like this in the ...
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### Expected Predicted Error (EPE) with L1 loss

In Element of Statistical learning it is saying on page 20, equation 2.18. That using the L1 norm instead of the usual L2 norm leads to an $f(X)$ optimising the EPE being the median instead of the ...
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### Simple Log-likelihood question

I've got a simple question about deriving log-likelihoods. I am stumped by the following--> If the log-likelihood is: 𝑙(𝜆1,𝜆2) = 𝑦1 log(𝜆1𝐹1)−𝜆1𝐹1 −log((𝑦1)!)+𝑦2 log(𝜆2𝐹2) −𝜆2𝐹2 −log⁡ (...
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### Maximize profits by setting price

I am working on a model to set a price that maximizes profits. The equation for profits is: Profits=price x (# sold) - (fixed cost) x (# sold) I have models ...
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### Finding the slope at different points in a sigmoid curve

This is my data. x <- c(0.5,3.0,22.2,46.0,77.3,97.0,98.9,100.0) plot(x, pch = 19) I want to fit a curve through these points and then calculate the slope at ...
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### Can Regularization by achieved using Relative Sensitivity?

In a Mathematical Model we measure the sensitivity of the output with respect to the parameters and it is desirable that a small change in a parameter doesn't lead to wild fluctuations in the output ...
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### Under the 0-1 loss function, the Bayesian estimator is the mode of the posterior distribution

My notes are rather light when it comes to this topic. I understand that the bayesian estimator, defined as (for sample space $\hat{x}$): \$E[\Theta | \hat{x}] = \int_{ \forall \Theta}yf_{\theta|\hat{...