Question

Let X be a discrete random variable that takes on the Ivalues - 1,0lt and suppose P ( X = -1) =P ( X = 1) = 75 A. Find the moment generating Function Mx (t) of x. B. Use the moment generating function to find a formula for the nth moment E(X") of x.

plz explain

Answer 1

Solution: pCX=-1) = 's a P1x=1). I. Moment na generating function. function. Moment " My Ct) Elet2) = e. p(x=2) C = -1,1 = e. p(x=-1) + ei pcx=1) jete jet - j [e*ret] My Ces = aj les ext] f -EL My Ct) = Ś [etej CU - at tao y-1 -0. - Cebu 1 et Yetu 3:410 at tao . E(XP) Micos as basa en lettere at too sete "far too = $# -2 = 1+1=2 t -t e te Tattoo رہی ہے د: ده مه ) سے لے odd so. if nis E(x) = cs:Scanned with med Elx") = ſ 2 , If n is even.

ie: M ents Moments froom mgf 6Cxo) meco). E (x ) = GCX) is derivative of first with respect to t and then put too. E(X)=0 from above Similarly My Co) 286 is the second derivative of My Lt) winito ot and put too as G(XQ) =2. € (x 3) = 0.3 My(O) = et. et of tao 23t e ou Niccanja ſo if nis odd if nis even. Scanned with CamScanner