Let Y be a random variable with MGF:
mY (t) = e (e t 2/2−1)10 = e (e t 2 2 −1)10 = exp((e((t^2)/2)− 1)10) = exp ((exp (t2 /2) − 1 )10) (The same expression has been written several times to hopefully make it readable.) Use Tchebysheff’s Inequality to give an upper bound on P(|Y | > 4).
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