Data Delight

The probability density function ( pdf ) and cumulative distribution function ( cdf ) are two of the most important statistical functions in reliability and are very closely related. When these functions are known, almost any other reliability measure of interest can be derived or obtained. Figure 1 Figure 2 PDF - Probability Density Function or density  of a continuous random variable , is a function  whose value at any given sample (or point) in the sample space  (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample In a more precise sense , the PDF is used to specify the probability of a random variable falling within a particular range of values , as opposed to taking one value.   CDF -  cumulative distribution function  ( CDF ) of a real-valued random variable   X, or just  distribution function  of  X, evaluated at  x, is the probability  that  X will take

                             Sigmoid function Equation Definition  Technical Wikipedia Definition :  A sigmoid function is a bounded , differentiable , real function that is defined for all real input values and has a non-negative derivative at each point  and exactly one inflection point. Simple Definition - It is basically a 'S' curve or activator function which is commonly used in Machine Learning, it is used to bound/transform/squash a wide range of values within [0,1]. Basic illustration of how Sigmoid Function works, Defining the Input - Array containing 99999 equally spaced numbers between -10,10 Defining the Sigmoid Function -  Plot of the transformed values -   Graph between input and transformed output                                              Distplot of the Transformed values As we can see from the above plots the values are bounded between 0,1 for any given value. Plot if it had been e^x instead of e^-x : Now going back to the Technical Definition, A sigmoid