Let XXX have PDF f(x)=1/2f(x) = 1/2f(x)=1/2 on [−1,1][-1, 1][−1,1]. What is the MGF MX(t)M_X(t)MX(t)?
et−e−t2t\frac{e^t - e^{-t}}{2t}2tet−e−t
sinhtt\frac{\sinh t}{t}tsinht
cosht\cosh tcosht
Both a and b