Hello
E(x) is simply given by summing x*f(x) for all x in case of discrete distribution like this one.This gives
E(x)= (-3)*(.05)+(-2)(0.10)+(-1)(0.30)+0+1(0.30)+2(0.15)+3(0.10)= 0.25
Since E(x) is a linear transformation, we can write
E(2x+3)= 2E(x)+ 3 = 3.5
and E(2x-3)= -2.5
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