$5$d$)$ Applying the approximation: Example $1$

In the case $N=100$ and $=0\mathrm{.}5,$ write an expression that evaluates to the approximate value of $P(T_{N}4)$ based on $5b.$

Complete the cell with just one expression, not multiple lines.

$N=100$

theta $=0\mathrm{.}5$

# Approximate value of $P(T_{-}N4)$

return $1-$ poisson. cdf$(3,$ np$.$sum$([$theta $/($theta $+k-1$ for k in range$(1,$ N $+1)]))$

Now compare this approximation with the corresponding empirical approximation based on the $5000$ simulated values sim$\_100\_$pt$5$ in $3$c$.$

Complete the cell with just one expression, not multiple lines.

$\frac{?}{?}$# Empirical approximation $toP(T_{-}N4)in$ the case $N=100,$ theta $=0\mathrm{.}5$