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exponential function - Intuitive Understanding of the constant $e . . . I know there are many ways of calculating (or should I say "ending up at") the constant e How would you explain e concisely? It's a rather beautiful number, but when friends have asked me "what is e?" I'm usually at a loss for words -- I always figured the math explains it, but I would really like to know how others conceptualize it, especially in common-language (say, "English")
Proving $\operatorname {Var} (X) = E [X^2] - (E [X])^2$ I want to understand something about the derivation of $\\text{Var}(X) = E[X^2] - (E[X])^2$ Variance is defined as the expected squared difference between a random variable and the mean (expected v