$5$e$)$ Applying the approximation: Example $2$

The calculations above should indicate that the Poisson approximation to the distribution of $T_N$ is pretty good. Now try it in a case where we don't have an empirical

approximation for comparison

In the cell below, find $E(T_N)$ in the case $N=1000$ and $=0\mathrm{.}7$

N $=1000$

theta $=0\mathrm{.}7$

return poisson.cdf$(9,$ np$.$sum$([$theta $/($theta $+$ k $-1)$ for k in range$(1,$ N $+1)]))$

With the same parameters $N=1000$ and $=0\mathrm{.}7,$ approximate

Complete the cell with one expression, not multiple lines.

# Approximate value of $P(T_{-}N<mn>1</mn><mn>0</mn><mi>)</mi>$ in the case $N=1000,$ theta $=0\mathrm{.}7$