\documentclass[a4paper,12pt]{article}

\usepackage[english]{babel}
\usepackage[latin1]{inputenc}
\usepackage[dvips]{graphicx}
\usepackage{url}
\usepackage{amssymb}

\parindent 0mm
\parskip 3mm

\pagestyle{empty}

\begin{document}

{\textbf{T-122.103 EXERCISE 3/2003}}

In T4 on 3 October 2003 at 12:15--14 o'clock.

\begin{enumerate}


\item 
Consider the problem of finding what fraction of rows in a 0-1 database
satisfy a given Boolean formula. For example, denote by
$g(A=1\vee B=1)$ the fraction of rows that have $A=1$ or $B=1$.
Express $g(A=1\vee B=1\vee C=1)$ in terms of frequencies of sets
(i.e., by using $f(X)$ for suitable sets $X$).

\item
Generate random event sequence data containing 10 different types of
events and altogether 10,000 events. Compute for all pairs of events
what is the probability that they occur together in a window of size
$W$, for suitable widths $W$.

\item
Consider an event sequence containing events of types $A$ and $B$,
distributed uniformly at random over the time interval. Let $n_A$ and
$n_B$ be the expected number of events of types $A$ and $B$ occurring
in a unit interval, respectively. Compute the probability that a
window of width $W$ contains both $A$ and $B$.

\item
Study the definition of $J$-measure on page 25 of the course material,
and explain the motivation behind it.



\end{enumerate}
\end{document}


