parameters - Statistics: Maximum Likelihood and Method of Moments -

i trying find maximum likelihood estimators , method of moments of following:

g(x;w;s) = pdf =  1/we^((-x-s)/(w)), x > s 

for finding mee of s , w, know have solve following 2 functions:

(1) xbar = mu  (2) 1/n summation xi^2 = mu^2 + var 

i found e[x] = mu = integral s infinity x*1/we^((-x-s)/w)dx =

e^(-2s/w)(w+s) 

i found e[x^2] = var = integral s infinity x^2*1/we^((-x-s)/w)dx =

e^(-2s/w)(2w^2+2ws+s^2) 

from here have 2 equations:

(1) xbar = e^(-2s/w)(w+s) (2) 1/n summation xi^2 = mu^2 + e^(-2s/w)(2w^2+2ws+s^2) 

now know need solve 2 systems of equations, having difficult time solving them. wanted solve first equation either w or s, , substitute second equation, cannot figure out. wondering if integrated on correct bounds? made sense me, might wrong. since couldn't further using mme, attempted method of maximum likelihood , got following:

p(x1=x1, x2=x2,...,xn=xn) = p(x1=x1)p(x2=x2)...p(xn=xn) = g(x1;w;s)g(x2;w;s)...g(xn;w,s) = 1/we^((-x1-s)/w) * 1/we^((-x2-s)/w) *... * 1/we^((-xn-s)/w) = 1/w^ne^(-1/w summation xi+s) 

from here again stuck , i'm unsure if did correctly. don't know if did makes sense anyone, appreciated! :)

thank everyone! lizzie

p.s. i'm sorry it's hard read math problem in format typed it, i'm unfamiliar website.

recheck integrals. e[x] = mu != x*1/we^((-x-s)/w)dx rather equal x*1/we^((-(x-s)/w)dx = s + w. guess other errors follow because of mistake in carrying forward sign: -(x-s) = -x + s.

by way, density function corresponds shifted exponential distribution. because if take x exponentially distributed mean w x-s has density given g.