Could you please change your $\Phi (x)$ notation to some other notation? $\Phi (x)$ is commonly used to denote the cumulative probability distribution function of the standard normal random …

53 I have a dataset from sklearn and I plotted the distribution of the load_diabetes.target data (i.e. the values of the regression that the load_diabetes.data are used to predict). Using Python 3, …

15 As explained in Gortaur's answer a delta function cannot be the probability density function of a real random variable. Nevertheless sums of delta functions can be viewed as the "missing …

132 How to calculate probability in normal distribution given mean, std in Python? I can always explicitly code my own function according to the definition like the OP in this question did: …

So I need to calculate the joint probability distribution for N variables. I have code for two variables, but I am having trouble generalizing it to higher dimensions. I imagine there is some …

Because dF (x) (CDF) is continuous function in either cases; f (x) is discrete or in case f (x) continuous. In other words, in case of f (x) is discrete F (x) would be like as a step function [as …

scipy does not come with a function to calculate log likelihood (although MLE method is provided), but hard code one is easy: see Is the build-in probability density functions of …

Theorem: Two identically distributed independent random variables follow a distribution, called the normal distribution, given that their probability density functions (PDFs) are known to be …

When considering the bell-shaped probability distribution function (PDF) of given mean and variance, the peak value of the curve (height of mode) is 1/sqrt (2*pi*var). It is 1 for standard …

The mean is the point of balance, which is basically the center of mass if the probability density function was solid. Median = $\int_ {-\infty}^M f (x) dx = \frac {1} {2}$ or the area equals 1/2 …