        \problemdata       % Takes 5 *mandatory* arguments
        {variance-6}             % latex-friendly label for the prob.
        {variance}               % The topic of the problem content.
        {Velleman}               % Source (if known)
        {S98 PS11-7; F97 PS11-8} % Usage (list ones you are aware of).
        {Theory Pig, S02}        % Last revision info (author, date).
%BEGIN Tina's problems
%%%%%%%%%%%%%%%FALL 99 %%%%%%%%%%
\begin{problem}%{\bf fall96 }

Use the lecture notes to compute upper bounds on the
following probabilities:

\begin{problemparts}
\problempart 
In a poll with 2000 people, what is the probability that the result is off
by more than $1\%$?

\solution{$\prob{\geq 0.01} = 1 - \prob{< 0.01} \leq 1 -
\left(\frac{1-0.01}{1-0.02}\right) 2^{-2000} \binom{2000}{0.01\times
2000}$}

\problempart
In 1000 independent coin flips, what is the probability of getting 
at least 600 heads?

\solution{ $\prob{\geq 600} = 1-\prob{< 600}(n=1000,\alpha=3/5)\leq 1 - 
2^{-1000}{\binom{1000}{600}}{\frac{1-3/5}{1-6/5}}$}


\problempart
In a noisy communication channel with $10\%$ error rate, what is the
probability that out of 1000 transmitted bits, at least 200 bits are 
wrongly transmitted ({\em i.e.}, {\tt 1} is received as {\tt 0} and 
vice versa)?

\solution{
g$\prob{\geq 200} = 1-\prob{< 200}(n=1000,\alpha=1/5)\leq 1 - 
2^{-1000}{\binom{1000}{200}}{\frac{1-1/5}{1-2/5}}$}

\end{problemparts}
\end{problem}
