$S=$ current stock price, $r=$ annual mean return on a stock $($decimal$),=$ annual mean return

on a stock $($decimal$),dt=\frac{1}{252}($ie$.$ one trading day$)$ and $q=$ risk$-$neutral probability of an $"$up$"$

move in the stock price. U and D represent the $"$up$"$ and "down" moves $($over one period$)$ in the

stock price. $E{S}_1$ is the expected stock price in a "risk$-$neutral" world after one trading day. Using

the BOPM and risk$-$neutral valuation, which of the following equations is true?

a$.E{S}_1=qSD+$qSU$=$Sexp$(r.dt)$

b$.E{S}_1=qSD+(1-q)SU=$Sexp$(r.dt)$

c$.E{S}_1=qSD+(1-q)SU=$Sexp$(.dt)$

d$.E{S}_1=$qSU$+(1-q)SD=$Sexp$(r*\sqrt[\phantom{2}]{dt})$

e$.$ None of the above