as we know that mgf of a discrete varible Mx(t) =P(x=x)*etx
comparing it with given MGF:
P(X=0) =0.6
P(X=-8) =1/5 =0.2
P(X=1) =1/5 =0.2
hence E( ) =xP(x) =(-8)1/3*0.2+01/3*0.6+(1)1/3*0.2 =-0.4+0.2 =-0.2
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