Continuous Probability Distributions

Introduction

$$ We \ studied \ some \ important \ continuous \ probability \ distributions \ such \ as \ normal \ distribution \ and \ uniform \ distribution \ in \ previous \ classes.In \ this \ chapter \ we \ will \ study \ the \ other \ different \ continuous \ distributions \ Cauchy \ distribution,gamma \ beta,exponential,Laplace,lognormal,logistic \ and \ weibull \ distributions \ along \ with \ their \ properties \ and \ uses \ which \ plays \ vital \ role \ in \ Mathematical \ Statistics. $$

Cauchy Distribution

$$ It \ is \ also \ one \ of \ the \ continuous \ probability \ distributions. This \ distribution \ plays \ an \ vital \ role \ in \ illustrating \ various \ theoretical \ aspects \ of \ probability \ theory \ and \ Statistics \ rather \ than \ practical \ applications. $$

Definition: $$ A \ random \ variable \ X \ has \ a \ general \ Cauchy \ distribution \ with \ parameters \μ \ and \λ \ if \ its \ probability \ density \ funtion \ is \ given \ by $$

$$ f(x)=frac \{1}{π}$$