Uniform distribution: continuous vs discrete.

easy

Answer

$Discrete: U{a, ..., b} — each of (b-a+1) integers has probability 1/(b-a+1).$
$Continuous: U(a, b) — density 1/(b-a) on [a,b], zero elsewhere.$
$\operatorname{Var}(X)\; = \;(b - a)^{2} / 12$
$(\mathrm{generate}\;\mathrm{any}\;\mathrm{distribution}\;\mathrm{by}\;\mathrm{feeding}\;\mathrm{uniform}\;\mathrm{samples}\;\mathrm{through}\;F^{-1})$

Check yourself — multiple choice

Var = b - a
Discrete: 1/n over integers; continuous U(a,b): pdf 1/(b-a), E=(a+b)/2, $\operatorname{Var} = (b - a)^{2} / 12$ ; base for inverse transform sampling
Only continuous exists
Undefined mean

Uniform: pdf 1/(b-a); $\operatorname{Var} = (b - a)^{2} / 12$ ; base for inverse-CDF sampling.

#distributions#probability

215 interview questions in this topic.