16.5 Let Bt be a standard Brownian motion started at 0. Use that for any function f we have:

E[f(Bt)] = 1

√2πt  ∞

−∞

f(x)e− x2 2t dx, to calculate:

E[B2k t ]

for some k, an integer. As a hint, you may want to use integration by parts and induction to come up with a formula for E[B2k t ].