# Stock Price Problem Question

It a simple school problem with five different parts. I understand a), b), c), and e); however I am very confused on what d) means. The problem goes like this:

"Suppose that each day the price of a stock moves up 1/8 of a point, moves down 1/8 of a point, or remains unchanged. For i>=1, let U_i and D_i be the events that the price of the Stock moves up and down on the ith trading day, respectively. In terms of U_i's and D_i's, find an expression for the event that the price of the stock: d) is the same as today after three trading days;"

What I do not understand about d) is that is it saying the price of stock has not changed and has remained the same across all three days (or possibly four because of the 'today' part)?Could it possibly mean that the stock has been steadily rising or falling for the past I don't know how many days. Is it saying that it is the same trend as of three days ago? Could someone please help clarify this for me?

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+1 for a nicely phrased question. Because this is a homework/self-study problem, could you add the self-study tag to your question? See stats.stackexchange.com/tags/self-study/info – Patrick Coulombe Aug 29 '14 at 19:52

Some numeric examples (3 made up histories for the price of the stock): $$\begin{array}{cccc|c} \textrm{Today} & \textrm{After 1st day} & \textrm{After 2nd day} & \textrm{After 3rd day} & \textrm{Comparison} \\ 1 & 1 \frac{1}{8} & 1 \frac{1}{4} & 1 \frac{3}{8} & 1\neq 1\frac{3}{8} \\ 1 & 1 \frac{1}{8} & 1 \frac{1}{4} & 1 & 1 = 1 \\ 1 & 1 & 1 & 5 & 1 \neq 5 \end{array}$$